This has resonance with a past idea of mine regarding revamping the fordable natural streams. Instead of being a channel into Z-1 but a walkable surface, as they currently are, they could be merely floor tiles of 'stream' (as opposed to natural ground, but perhaps retaining "on a bed of <ground-type>" qualities visible or otherwise) equivalent to 1/7ths depth but with a little less propensity for evaporation than you'd normally find. (Or they'd be effectively evaporation-proof due to having a continual source, but even then, in hot climates they might run dry, leaving "dried stream-bed" tile...?)
As a natural (and world-genned) feature, I also sort of imagined a deposition/erosion cycle allowing slow changes to whatever pathing the watercourse took, depending on the material of the ground it is flowing past, and whether there are native or built walls/slopes neighbouring it, and leaving an appropriate sedimentation soil-type behind when it moves. It could then flow into and attempt to fill dwarf-dug channels (or natural hollows) if it drifted over that far. On Z-1, you wouldn't notice a thing (except a damp ceiling giving you the usual Z-1 from water warning) except where there was an opening of some kind (channel/stairs/ramp) between them, in which case it would pour through (and effectively decommission the down-stream parts of the original stream path as it passed through the sink-hole instead).
So... I think you're describing that, give or take a detail, for your "Shallow Channel" suggestion. Whatever the current state of the floor, expend an extra material to make it a 'foot-bath' depth of water, perhaps, and thus resiliant to erosion and repathing (though if fed from a 'natural' stream or river it might be fun to have to clear out sedimentation at procedurealy determined twists and turns, or risk miner flooding over).
How to feed (my version of) your shallow channel, though? Most water sources you might use are up to 7/7ths deep or on the level below (and pumps would create a 7/7ths height on the channel's Z-level) so would over-supply your watercourse. Maybe a specialist building such as a sluice-gate, built to similar spec as the pump object, in game (visually, I can imagine a "-" or "_" and "=" featuring) that can be (manually, or mechanically controlled) made to deposit
just 1/7th of water onto a suitable prepared (or otherwise?) outward side as long as there is more than 1/7th on the inward one.
And of course misuse of the shallow channeling (not properly defining edges or ends to such a channel) could mean that your pleasant 'foot-bath' became a potentially level-wide feature draining down every stairwell it could reach before evaporating and gradually filling up the lower levels. (With great power come great responsibility. With new irrigation methods, there should come enhanced possibility of messing it up.
This could also tie in with a farming expansion. At least with certain crops. Whether it's some crops that will only grow on designated field tiles touching/within a given distance of a shallow channel with water at least at the start of a given season, or something rice-like or marsh-liking whose fields of cultivation
must be placed on shallow-channel tiles with a fairly constant (or at least regular) supply of water.
But I believe the current solution being arranged for easier water management and cross-fort transfer is pipework-based, running alongside pedestrian traffic in routable corridors and spaces, etc, which might also satisfy your original need.