1. You should be able to bypass the initial Verizon activation screen and upgrade to ICS over WiFi since the update is pushed out by Motorola from their servers. After the ICS update, you should be able to use your GSM SIM (needs to be a micro SIM) in Peru. That said, there have been instances in the past where users have reported problems using unlocked global phones that had never been activated on Verizon. This may not apply to the MAXX since the SIM slot will already be unlocked (unlike previous Verizon devices that required a code or action from Verizon to unlock the device). So, I think you'd be fine, but there's a slim chance of problems.
2. There shouldn't be any problems with this. As I already mentioned, the updates are pushed out from Motorola, so you shouldn't have any problems updating to ICS over WiFi and using the phone in Peru.
3. I think this is your best bet of the three. There shouldn't be any room for any problems going this route. Everything should work just fine.
And, again basing things off every other global Verizon device I've used or read about, once the phone is unlocked, it's unlocked forever. There's no limit on the number of SIM cards that can used, nor is there a need to connect to a valid Verizon account to maintain the global capabilities. The unlock is permanent.
If you really want to go with a brand new device, I would suggest looking for the international RAZR MAXX that comes GSM unlocked. You can purchase one of those online for around the same price (or slightly more) as buying a brand new Droid RAZR MAXX. It also won't come with all of the potential hassles in dealing with a Verizon phone abroad when you don't have Verizon service as it's intended to be an unlocked GSM device. But, if you're looking to save a few bucks by picking up a used device, going with a Verizon MAXX that already has ICS installed will be your best bet. You should be fine in any of scenarios you mentioned, but I think going for one that already has ICS, and has already been activated on Verizon, will be the safest route.