" I tested without removing from board (I hope this is OK). "
It's not the best way, of course, but for now we can think there is enough, if capasitence close to the right value...
So, if this capasitors good, then ... i want to see picture from oscilloscope. First from +12V power lines with main connected. Do you have it?
So, its strange, if on mainboard you don't have some "burning" components, but on main filter capasitors "jumping" voltage ... strange, strange... may be problems with PFC. Do this TV have PFC? Need to look schematics...