Companies such as USAA have complete deployment checklists. Deployers call them before departing, set up auto-pays, file powers of attorney for spouse or family members, opt in for electronic documents, get a deployment marker set on their account so USAA would know they were not easily reachable.
I was on AD for 26 years and never had snail mail problems. I dealt with USAA and NFCU. Military-friendly companies understand crazy military life. Much of that was when everything was snail mail.
If you google "mail forwarding services," there are any number of companies who cater to RVers, world boat voyagers, international travelers/workers, etc. A US mail address is provided, and the service bundles the mail and sends it where requested. I know that's how they work. I never needed it.
Military families become aces at change of address routines. If they are going to be TAD/TDY for a few months here, a few months there, they might use a family member's address. Family member can box it up and send it to the command, marked for the military member. There is always a "mail plan," which helps members understand what the arrangements are for deployments, overseas rotations, extended periods in combat zone or without personal comms.
Military folks have been dealing with mail since ancient times, so there will be plenty of advice from experienced hands about options.