I agree with you that if the fluid is dropping down to where you can see the top of the core, you have an issue to sort out.
You have done a compression test which is good. If you have access to compressed air, I think you should carry out a leak-down test to rule out a leak of coolant into the combustion chambers. A compression test may only show that type of failure when it is extreme.
Hmm, I'm not sure....if he's running with no stat he could have localized boiling on number 1 that would be enough to cause his issues, I have a big diesel 4x4 that does the same thing, always drops it's water down to the level of the top of the cores, but if I look, with the engine cold, the top hose is under vacuum, but the vacuum isn't enough to draw water back through the rad cap to top itself up again. This vehicle gets really heavily abused in real tropical conditions and never gets close to overheating, it also never uses any coolant after it's sorted itself out and found it's own level.