Yes, the store hours are one of the sadistic aspects of the game. Rather than time traveling all the time, consider doing a one-time time shift to better fit your schedule. Keep the Wii time correct and just change the time in the game once and leave it that way (well, unless your schedule changes).
From what I've read, turnips only rot prematurely if you repeat a time in the past. As long as you never overlap a time you've already played, your turnips won't rot prematurely. They'll still rot if you don't sell them by the deadline, though.
You might already know this but Nook will offer you a choice of variety, hours, or balance at some point. Don't say "hours" unless you want him to downgrade back to Nook 'n' Go! Picking "balance" will downgrade him to Nookway. Variety will keep Nookington's. People often pick "hours" thinking they'll get a Nookington's with better hours and then they're shocked a week later when they see a Nook 'n' Go gracing their town once again.