Use priority-of-dig-designations smartly.
Also perhaps make a burrow for just one miner, that contains this excavation volume (area-wide and depth-wise) whilst confining any other miner(s) to the next-most-favoured project area (at a pinch, a second and directly adjacent section of cavern, but be a little careful of the interface between the two if one goes qu7ickers than the other)
Ignore designating the uppermost level that you want to mine out, entirely, but paint stripes (or ever-decreasing perimeters) of Priority 1, 2, ...7 ramps on the next Z down, continuing with 7s when you run out of (lessening-)priority levels. For maximum micromanaging, as soon as all Priority1s are complete, repaint Priotity2s as Priority1s and so on (up to last necessary or first 7s, whichever comes first) but as long as you reprioritise what's left back to 1..7s before they get to the 7s proper you don't need to be quite so attentive.
An alternative (can work with multiple diggers) is stripe one area 1,3,5,(7s), and another 2,4,6,(7s) and know that they'll complete one stripe/set (the odds) before switching to the other stripe set (the evens) then you can draw them back to the 3s-now-1s after a little nibble or leave them be to shuttle both ways until just before both 7s are the next on their priority lists.
Depending on what side access/egress you have for them¹, you can also put priority(N+1, or N+2) on the Z directly below the priorityNs, as well as adjacent, and you'll nibble away more and more rock between enforced reprioritisation-micromangements (for a depth equal to to width, you'll have a one-low-edge to opposite-high-edge 'face' at the maximum extent, going by lines, though it's different if you're cutting an 'inverse pyramid' away, inside out or outside in). This mostly saves you your effort, and doesn't much speed things up or slow them down, either way, except for maybe how far occasionally they have to trek to cut the next ramp of the same priority.
But it's easier to do than describe, and there are pitfalls (not actually literally, if you're doing it right, but potentially literally if you've done it slightly wrong) but the biggest risk is when self-trapping themselves and you've not got a good method of emergency-escape prepared (another digger prepared to slice in from the side, perhaps) if they suddenly get over-hungry/thirsty because of the scale of your demanded void overwhelming their preparedness for isolation.
An unself-trapping method could just include a column of stairways dug to send them to the top (that you use 'remove-stairs' upon, instead of ramping, in that column only, but in with the same priority scheme) so that they always have the exit to the imtended low-level door. Or whatever mid-level entrance you've decided will give you (stair/ramp) access to the base of your fully-defined void.
I don't tend to use the Mark Only designations too much with this sort of scheme. The usefulness of redefining Marked designations for actual ones is less use when you know you're going to have to Designate for real with various changing priorities, though Marked-as-Priority7 is perhaps useful to keep you in mind of where you don't want to tunnel into inadvertently, for that water/magma-channel perhaps, because you're capable of forgetting you're eventually wanting to get that area. This is better (and quicker) than horizontally-mining whole floors outwards to define your extent with many-individual-open-layers and then trying to get rid of the floors between and having to avoid floor-falling.
And, anyway when you get to the bottom (with the purely-ramping method), finish off (if you wish) by designating for Ramp-Removal any dug up-ramps that remain at the final-floor level. If you strictly dig ramps from inner-core and sequentially outwards, the 'spare' inner ramps disappear when they're only adjacent to wall-adjacent ramps. The same for if you stripe from one wall to the other. If you do an outward-in perimeter dig, you'll be left with edge ramps to deramp and the central ramp (and/or final escape-stairwell-remnant).
(Much simpler, actually, is to just paint Priority1 ramps across the second-to-topmost level, P2s the level below that, etc, but don't try that until you're experienced enough to see where premature multi-digger application might leave orphan blocks around on higher layers that then get totally disconnectedly under-ramped by speedy co-diggers to the one that is supposedly enacting the former. Can be messy when a quick near miner gets busy on the next layer whilst a slow distant miner 'reserves' the last of the earlier jobs just after visiting the food hall or rising from a good sleep, unless you prepare for it.)
¹ An alternative to burrow-limitation is to have them dig away their own initial access point, so keep them in that burrow physically, but if it's a big excavation make sure they're fed/beered/bedded well enough beforehand so that they don't suffer too much as they work their way back to freeing themselves up again.