It might be odd for normal RTS/FPS players coming to the game, and annoying even to those used to DF's frame-rates going down upon the underworld collapsing (or a cat trying to get through a cat-proof door!) but it is just a simple(!) matter of putting select things into 'stasis' (or skip a proportion of their interaction calculations) as you say, and for everything
not slowed down (or the fastest thing 'sped up', normalising them to 'standard' and everything else, including time-of-day/date, relaxed to slow. Performance-wise, it should be
better...
...Frexample, you accidentally (or 'accidentally') breach an aquifer/water-source and it's tumbling down your fort's deep staircases (or, worse, magma, slower but with temperature changes too). Activating super-speed for the repair-squad will suppress the processor-sapping flood (and cats, invasions, whatever else is excluded from the 'spell' and you're actually experiencing a less-lagged control of those lucky few as you coax them to do whatever you want them to do.
That probably does require some degree of rewriting. A flag/multibit-flag attached to everything (individually and/or group) or alternately an exhaustive set of 'what time-treatment to apply' (or non-exhaustive one with a fall-back for anything unrepresented) that the kernel of the simulation must be primed to check to know whether it can/must skip the "this thing updates" process it normally attempts. (This is, on the whole, single-threaded so should have just such a leverage-point.)
Depending upon implementation (it may depend on the style of time-warping, and also of the nature of the entities concerned) this would have opportunity to be briefly checked and honoured when "another thing updates" is happening, and part of that is "push the first (paused) thing to be updated by it". e.g. An antagonist could shout all he wants at a frozen target, there'd be no 'has been shouted at by...' applied to them as it wouldn't sink in - unless as high-pitched buzzing. Though if the antagonist stabs them, assuming the magycks don't do
anything too protective, they'd experience wounds during their time of not being as up-to-speed as the stabber. If it's an area-effect application, heat from adjacent magma might just not be calculated to transfer inside the uncalculatable area, flows might stop against the barrier (or barely trickle through, on 'allowed' ticks) but if the instigator/master of the stasis-field has an exemption (special medallion? ...just part of their casting?) they could walk in and move round, pick things up (think the typical 'speedster in their own time-frame' set pieces from X-Men/The Flash/Heroes/whatever) and put things down, maybe do a limited amount of interaction with individuals (s)he finds there (no talky, definite stabby, possibly manhandle them over/away from a ten-storey drop if they could have so manhandled an unresisting individual normally).
Momentum/kinetics isn't really something we need to worry about, if we'd rather not bother Newton or Einstein about such things they never really considered part of their Real World formulae. Let's assume that throwing things that then merge into the slowpoked background effect/out of the personal speed-force bubble have throwing-velocity in the suppressed zone equivalent to that imparted in the unsuppressed one, to be evident only as the slow time takes its next active ticks or the frozen time becomes dispelled. To be fair, it could also be vice-versa, but as part of the 'superpower' invoked you could assume that the individual with the personal time advantage
could indeed pluck crossbow bolts from the air, just by being clever with the 'field', they control around themselves, either to just deplete the trajectory entirely and place them on the floor or move/rotate them and somehow impart/restore an equivalent motion upon them as you leave them flying towards their new target/their origin. (Consider it a Necessary Secondary Superpower, though if I could at all theoretically apply finger-pressure to a 'time-locked' bullet, already, I should indeed apply over a reasonable amount of my own time a force that 'feels' like a sufficiently large instantaneous impulse, and the skill may only lie in 'feeding' it just the right amount of push to be going back in the right direction - and tweaks to impart the correct non-tumbling spin to it.)
For the "putting right what once went wrong" scenarios, the only real way is to effectively have a savepoint (if it's a planned opportunity/forced-mission, easy to establish a likely moment, or tie into the existing Seasonal Saves mechanic) and then when fate/your decision decrees you have to enter the wibbly-wobbly time-tunnel (having seen how the world has been converted into a crapsack one, and gained 'sufficient' knowledge of why, so maybe how to stop it) your character then plays through from the old save-point to make (you
hope) a diverging forward history that doesn't have Hitler winning/whatever. Then you either have a wibbly-wobbly path back to the date-of-departure/DoD-plus-mission-time (worldgen simulation is used to establish what new history you'll find when you get there, perhaps with the opportunity to return/redo the old-save-visit/add a further
more experienced you to your prior back-traveller's version of the save) or you just have to take 'the long way back', if you can.
Assume (because it essentially is) that you're starting off again (each time?) in a new universe, so getting your old self killed along the way isn't paradoxical, because you aren't trying to maintain the time-line[1], though if it's long enough ago (a savepoint made during worldgen) you might not even exist (yet, or ever). Or you mind-merge with your younger self and diverge with (increasingly unsure) future-knowledge sending you on another path. Or anyone/thing that goes back makes their contempetaneous selves/items that existed at that point in the past just absolutely puff out of existence because the Universe don't wanna have duplicates running around for Plot reasons. One way or another (or another, or another) Arrangements Are Made. And, yes, failure
is an option. The world could be Crapsackier. (Hey, maybe you could toady up to the antagonist, get in on the action. Or get a head start on them and do their thing
instead of them, only better! Like ban Wibbly-Wobbly Portal invocations/monopolise them solely for your own ends.)
Just some thoughts. I occasionally have them, as you can tell.
[1] You're actively trying to change it! The exception might be if your mission is to go back and get a 'lost' artefact that is the only known Kryptonite for The Big Bad, to use it against them in the Present. As far as the Quest is concerned, the Kryptonite was lost for unknown reasons, or destroyed by TBB, whereas obviously you're going to resolve this by being the one who 'rescued' it from the past (in circumstances mistaken for being lost/destroyed) and always had actually been the one to courier it into the then-Future/now-Present to send delayed Karma down upon your foe. Well, that's how a film-script would do it, tying up all the loose ends (doing a John Keel along the way, to your younger self, maybe), but the restrictions needed to apply such a Self-Consistent, Self-Reinforcing, Meta-Paradoxical Non-Paradox to gameplay would be... challenging and/or unattrarctive. Perhaps an enforced locality - ...at the time of your original history, you were not exploring near the Dark Lord's seat of power, as a black cloud of evil settled across his expanding realm, nothing but rumours escaping the benighted realm, and then before you are yourself overtaken by the fiendish fof you find the portal that leads back into that obscured and mist-tainted territory with no way (or opportunity) to go beyond the expanding frontier, nor attack any of the few figures whose history you had already learnt of as inhabitting the infernal interior... You must complete your necessary trials (and set in motion the downfall, including activating your first-time-rounder's temporal transit opportunity) before the point at which your external self starts this mission, or else it cannot be achieved
at all until that point, though all this time you've been gathering the components/knowledge necessary to try to resolve this, the final piece to the puzzle being the magic Ring Of Rewinding you first used to enter the past, but which had fallen off your finger as you did so, and now awaits you returning physically to the now overcome point of departure to rediscover it where it fell and combine its powers with the Sword Of Truth, the Shield Of Protection, the Helm Of Knowledge and the Mug Of Greatest Grandma In The World.
Or something like that. If you like that kind of thing.
(Resisted the feetnete long enough, then made one big doozy of one. Hope you like it!)