Would Electrum Server be a jumping off point for this sort of thing? I haven't looked at it in detail, but it seems like it's trying to accomplish much the same thing, though with less constrained bandwidth.
Alot of sailors and remote expeditions depend on https://winlink.org, would be so cool if we had a similar network for Bitcoin.
- TXN Broadcasting gateways
- BBS for Block height/difficulty, fee rate, supply
- ZeroLink when comes out will help with building txns with minimum sync
Don't need much just enough...

Discussion
This is not like "internet". It's extremely low bandwidth.
No, I understand, I've played around with WinLink a little. I just meant that Electrum has got some of the low hanging fruit of remote/constrained connectivity solved, use that as the beginning.
I'd think at a minimum you'd need a way to:
1. Request UTXOs for a given address
2. Transmit transactions
3. Verify fee rate (of the last few blocks?)
Good point.