To put it into perspective:

https://solarsystem.nasa.gov/moons/saturn-moons/titan/overvi...

According to this (at the time of reading) a one way trip at the speed of light is ~75 minutes, so you will have approximately two and a half hours of ping.

Ouch.

Still, it raises an interesting question: how would a hypothetical Earth-Titan network protocol work?

That protocol exists, it is called Delay-Tolerant-Networking.

http://ipnsig.org/wp-content/uploads/2015/05/Whats-new-in-IO...

Can't do much about the time it takes light to get here, so I guess the answer is we'd have to learn to love 75 minute ping :)

Alcubierre warp drive powered Sneakernet?

If you can't be with the one you ping, ping the one you're with.

The InterPlanetary File System is a thing, it just isn't interplanetary yet: https://en.wikipedia.org/wiki/InterPlanetary_File_System

Batch instead of stream I'd reckon.

Perfect for mining bitcoin

Not really; if you find a block it will mostly likely have been beaten by someone else's block by the time yours reaches most nodes...unless there is a Saturn based side chain or similar.

This will sound crazy, and I'm not suggesting the consumer would deal with it directly, but I think we'll need coins for each planetary body and another one for the solar system that has a much longer block time. More scales would be useful, but these are the minimum. Repeat for each star, with MilkyWayCoin having an absurd block time.

It depends if the "most nodes" are on Mercury or on Earth.