This morning I was able to have a QSO with a station in Northern Ireland for several minutes. This was running the Q5N2 with no help and with the Zetagi MB+5 mic instead of the stock mic. I think that's probably telling me there is nothing fundamentally wrong with the radio itself.
I have another radio due to arrive today to keep in my "shack", such as it is, to help me with this type of debugging/diagnostics. It's a President Mckinley USA version. I was going to get it for the truck but decided against that. I may hold off for a few months and see if a President Lincoln III shows up with similar specs (but lower power I am sure, which is fine) to the Q5N2. I had a Lincoln II briefly but got rid of it when I got the Q5N2. I should have kept both!
I think the McKinley has a 6 pin mic so I might be able to try it on the Q5N2 using the RJ45 adapter as well and see how it does. If/when I get all that sorted out then I will add the KL503HD to the Q5N2 mix. I will also try the McKinley with the KL503HD because I am quite sure it will not overdrive the amp.
Good news is this is giving me a great excuse not to do any of the 100 things on my honey-do list. I am still definitely going out for lunch with my daughter though because that type of stuff is always at the top of my list (visiting with my kids and eating).