Convergence problem - NOT STK ICs / resistors

I really hope someone can help me with this.
Our LG RT-39NZ40RB rear projection TV has massive convergence problems ever since I ran the "Auto Convergence" feature after moving houses. Jumping onto the most obvious solution, I have already replaced both STK392-570 ICs (and checked all feedback resistors), but the problem persists.
What is particularly curious, and I unfortunately didn't notice this until now, is that the menu on-screen display is out of convergence as the rest of the picture when there is an input signal, but when I switch to an input that doesn't actually have a source connected, e.g. AV4 or the Component inputs, the OSD is perfectly crisp with all 3 colors in line. At the same time it does not make any difference whether the input signal is TV via aerial and tuner, an XBOX via Composite cable on AV1-4 or the same console on either of the two Component inputs. If there's a signal, the display is out of match, no signal and all looks fine.

As I said, I wish I had noticed this earlier as it is pretty obvious that the actual convergence mechanism has been working all along or why should the OSD work without input signal.

Now, what else might be the actual cause here?
I sure hope there's an obvious solution to the problem that I can fix with a little more DIY so that the new STKs haven't been a complete waste.

Thanks in advance for any ideas, Andy