Well for standard campaign testing, I suggest testers make a thread for their current campaign they are testing, and do an AAR-style coverage it. Update every few turns, provide screenshots, write down notable things, as well as first impressions; also report bugs and state opinions freely, accompanied by any possible suggestions etc.
As for battles testing, well, a mini AAR of the battle along with the ending stats scroll for all the units would suffice I think, that way we could keep track of the balance of the factions rosters, see if anything stands out either as too underwhelming or overpowered, and put it back to place.