Perhaps it is indeed a straight gun...Do you get any beam to the screen with NO magnet?
"I have one unrestored set that has a good original 12LP4 in it. I hate to take it out but I may have to eventually try that."
It seems that many times the most difficult experiment yields the most useful data!
Since you mentioned charging effects, I had another terrible (perhaps far fetched) thought about the key-stoning/focus... since the tube is not aluminized, is the landing energy of the beam constant as it travels across the screen ? Is it possible that the phosphor surface discharges somewhat during retrace?
jr