Powering "on" options

I would have thought that if you wanted, you could connect all the menu switches to your latching transistor (via a diode per switch, so they don't back-feed each other) as well as to a digital input - that way, you wouldn't need to use a dedicated switch.

Depending which Arduino you use, you may need to replace the bootloader (or do without a bootloader altogether) to get the boot time acceptably short.