AFAIK, the only way to truly turn them off is to remove the battery or cut the positive lead and splice in a switch. Only drawback is the switch has to be on for it to be able to charge, so that's a bit awkward. The "soft off" when you hold the power button is just deep sleep.
Mine frequently wake up from deep sleep but not after 5 minutes. More like 3-4 days. Which makes keeping a few always charged difficult.
Edit: I just checked the Power settings in the app (they've changed it a bit since I set mine up). The longest it can deep sleep is 72 hours it seems. Maybe yours is set to 5 minutes?
Well, the numbers I gave would be the same since those Meshtastic "modes" are just profiles for different LoRa settings, and the same LoRa Settings + frequency slot still applies (Meshtastic just runs on top of that).
I think what you're looking for is a dumb signal repeater, but I'm not super knowledgeable of the pros/cons/legality of those for the entire 915 MHz band. You'd be repeating anything in that frequency range, not just LoRa. And those also repeat noise the same as signal. Basically, it could end up making things worse in the long run by introducing noise.
Probably best to just coordinate with or start a community mesh group and settle on a specific frequency and LoRa settings.