A few different options that could be put into place in OneD&D because they are in other versions of D&D or D20 games
Level playing field: Everyone has the same allotment of resources with the same recharge rate. As long as everyone has the same, it doesn't matter in the slightest if it's a 5 minute day - all of the classes are still balanced against each other, and DM can then adjust challenge via the deadliness of encounters. 4e did this, with charactes having (outside utilities) the same amoutn of at-will, encounter, and daily powers.
Recharge out of player reach: If the players can't trigger a long rest during an adventure, this problem is moot. 5e does this with the Gritty Rest varient in the DMG, though that has issues with changing the expected number of short rests per long rest. Adventures in Middle Earth (a d20) does this by not allowing a long rest at all during the journey phase, with a few notable exceptions (a class feature, or finding a sanctuary like Elron's).
Recharge requires pushing on: This is a variant of above, where the characters can trigger feature and spell recovery, but it involved getting through enough encounters. 13th Age (a d20) does this, with at-wills, encounters, and "dailies" that come back at a full heal up - which only happens after four encounters. (13th Age does have a "players trigger it sooner", but it's in exchange for some campaign loss for the extra time spent.) This decouples sleeping from recharging, but it does work quite well.