In relation to the exile land ask, if the Golden Company does have “friends in the Reach” then couldn’t you could easily have two competing claims if one of the GC’s members has claims to lands owned by a Reacher lord who turns on the Lannister-Tyrell alliance, like a Tarly bannerman?

That second if is doing a lot of work. Here are the known members who might have land claims (other than Jon Con): 

• Franklyn Flowers (Fossoway)
• Marq Mandrake (Mandrake)
• Laswell, Pykewood, and Torman Peake (Peake)
• Dick and Will Cole (Cole)
• Jon Lothston (Lothston)
• Lorimas, Old John, and Young John Mudd (Mudd)
• Denys and Duncan Strong (Strong)

The Peakes are almost certain to be “friends in the Reach,” but they also have two castles’ worth of land that were taken away that the GC Peakes could split with their cousins, so that probably smooths the way. 

The Lothstons and Strongs both have a claim on Harrenhal, but given that both houses were said to have died out, A. there’s no one at home to compete with those claims, and B. those names are unlikely to be genuine.

The Coles probably lost most of their lands after the Dance, so there’s room there too. 

The Mudds are also a fake name, but Oldstones isn’t currently claimed by anyone as far as I can tell. 

We don’t know where the Mandrakes come from, so there might be a problem and there might not.