Well, I will simply assume you really don't believe that's an answer good enough. (Hint: if "all you have to do is not give them hours of downtime" that means "the whole adventure will be over, the sandbox emptied, in hours instead of weeks") Obviously you realize the value of a D&D-ish game to offer support for what you called the AD&D gaming style where you simply must rely on nightly rests - not in the short term (that's why we have Clerics) of course, but in the long term.
All I'm doing here is pointing out that far from offering advice on how to achieve this in their latest game, Paizo doesn't even seem to remember that the playing style exists.
I'm not much understanding your viewpoint as I don't recall hit point attrition being an issue for about 20 plus years now in D&D games. Can you provide examples in PF1 or 5E of an attrition style of play that doesn't use resource attrition like spell slots, combat healing, and daily abilities more than hit points past the low levels? Or are you primarily talking about low level play where a party runs out of resources much sooner?
I'm playing Extinction Curse right now. We've had to take quite a few days off after getting wasted by the encounters in that game due to resource attrition, specifically combat healing. You're making it sound as though your players are trouncing through Extinction Curse with Medicine like it's nothing. I'm not sure how they 're doing that given some of the encounters are very, very dangerous, especially so if you don't have the right means to counter them.