Been reading some of your posts and I'm impressed with what been done so far but I thought of some things I wanted to mention:
Instead of running out of time being an immediate game over / fail state perhaps have the difficulty increase:
Additional NPC's spawn and all NPC's gain better visual detection ability seeing as its daytime ... So not to make this an an infinite loop perhaps the character could faint from exhaustion if out for to long (maybe an extra 5 minutes on easy difficulty, 2 and a half minutes on normal difficulty and a 1 minute on hard difficulty)
I figure you have already considered multiple options to accelerate the growth of the character arousal - sex toys and specific clothing (using the term clothing loosely here - anything that can technically be worn does not necessarily need to cover up anything ... like shibari as an example) but perhaps remaining fairly close to NPC's back in revealing / no clothing could cause it to increase faster.
Ran into some problems with the 'find your clothing' scenario:The black shirt spawned on a dark colored patch of ground which meaning finding it was more luck then anything else - perhaps have the clothing spawn draped over objects instead or have something that makes them easier to find when you get close like the animation around the keys item in the 'find your keys' scenario.
Another bug in the 'find your clothes ' that occurred was if you find a character over outfit piece and wear it first then you cannot equip the under outfit item if you find it later - in this case I found the skirt item before the panties and could not equip the panties or remove the skirt to equip the panties followed by reequipping the skirt ... guessing an unexpected logic interaction as normally the character has to strip the outer layer before the under layer.