I've been running an FS2-powered campaign that is a little less cinematic and (slightly) more grounded than the standard, moving away from the standard setting to become more of a supernatural police procedural (cross the Rivers of London books by Ben Aaronovitch with the Bulletproof TV series by Noel Clarke and Ashley Walters, and that's sort of where we've ended up). Given that this has tended to result in a 'day-by-day' approach to timekeeping, as investigations continue, we've moved away from the "suddenly back at full health (except in consecutive scenes)" movie approach.
Under these house rules, characters heal Wound Points equal to an open Toughness roll (Impairment applies) each day (as long as they had some chance to look after themselves and rest - which is pretty much always). Use of Magic or the Medicine skill would be additional to this.
This still makes healing fairly fast, with the average character recovering from near-death in about a week, but no longer entirely miraculous, and that serious injury has a slight hangover (also allowing character to enthusiastically complain about injuries still hurting), but doesn't end up being entirely incapacitating.
Similarly, Fortune is recovered at a rate of one third of total (rounded up) per night's rest (not at some artificial point such as midnight, or dawn, more just "OK, it's the next day, you've recovered some chi, and your Wounds are somewhat better."
Another effect of this house-rule is that getting badly injured against the opponents can force the players to try to work out whether they can afford to wait until they're fully healed, or need to charge into the next likely fight. The first option might let the opponents move their plans further ahead ...
TL:DR version ...
At the beginning of every day, characters recover 1/3 (round up) of their Fortune stat, and heal Wound Points equal to an open Toughness check (Impairment applies, Fortune can be spent).