I go to the wilderness to get away from mobile phone reception.

I've got bad news for you:

https://www.iridium.com/solutions/land/

My understanding is that it won’t be particularly portable - the base stations are fairy large.

Last I saw, it requires an antenna that’s about the size of a television satellite dish. Maybe portable enough to stick on an RV or campervan, but almost certainly not something you can take with you while hiking or backwoods camping.

Sounds like it could easily sit in the bed of a pickup truck, or on the roof of just about any large cargo vehicle (like perhaps a Sprinter).

If they aren’t too expensive I hope to have one on a rural property as well as on the RV/truck I drive to get there.