i would do an ESR test of the electrolytics on the main pcb and the inverter boards. chances are you have several that are marginal, making proper operation thermally dependent and somewhat erratic.
Keep in mind that I don't know what any of that means (lol). But I do have a "multi-tester" (don't know how to use it) and know how to use a soldering iron.
Although I'm reasonably satisfied, this case is far from over and I'm still interested in getting to the bottom of this problem.
Also, it appears my transformer must be normal. This other boards transformer looks exactly like mine on the right side.
**broken link removed**
https://lcdalternatives.auctivacomm...nns-G-HSG1040-LCD-TV-Capacitors-P1841491.aspx