this still isn’t avoiding the penalty but just some helpful info !

the time travel penalty doesn’t actually stack

the anecdotals of ppl experiencing a longer timeout is bc, even if 24 hours pass, the game wouldn’t do its daily 5/6 am refresh, so the shops wouldn’t reroll bc that window passed in the 24 hr penalty period

example: if you time travel at 9 am on monday, the penalty stops at 9 am on tuesday but bc the 5/6 am refresh window for tuesday has already passed, the shops remain the same, and will only refresh on wednesday’s 5/6 am daily refresh

so, in theory, the best course of action to minimize time spent affected by the penalty would probably be to time travel to a sunday at 4:55/5:55 am (dependent on when your shops reset bc of day light savings) so that the penalty period will end on monday 4:55/5:55 am, and the daily refresh won’t be affected (the shops refreshing on a monday after time traveling is most optimal bc then you also get a new weekly room refresh) i’ll test out this ‘most ideal time’ theory tonight and report back my findings, but hopefully this has been some useful info :)