Signal sync problems with Sony TV

I have Indivision AGA Mk3 in my A1200 and have some problems with my TV, Sony KDL-40EX500. I have setup four modes: 1920x1080@50/@60 and 1280x720@50/@60 (setting as stated below).

The Workbench screen is normally rock solid in all of these modes. But some games that use same PAL settings have this issue that my TV loses the signal for a second or two. Problem is worse with 1080 settings but happens with some games also with 720 modes.

TV has four different HDMI ports and I have tested all of them, all with different HDMI cables (normally attached to different devices). There's a slight difference with the cables, for example Super Skidmarks' menu works fine in 1080 mode with the HDMI cable which was supplied with Nintendo Switch (I was told that this would actually be a very good quality?) but has problems with other cables. In 720 modes menu works fine also with all cables. But for example Pinball Fantasies table selection screen has problems with all the cables and both all the 1080/720 modes.

The thing is that I have tested this also with two monitors, my work monitor DELL U2412M and some other Asus monitor at my work (I don't know the model) and didn't notice any problems running those games. So it really seems to be some incompatibility with Indivision and my (old) Sony TV. In the other hand I haven't have any issues with the TV with the other devices that are connected to TV with HDMI: Nintendo Switch, PS3 and AppleTV 4k or the old Macbook Pro that I've used sometimes.

As I stated the Workbench screen is normally solid, but some times when I resize a window to be a very big the sync gets lost for a while. Also, if I enable the digital audio, I sometimes get a loud bang from the speakers when the screen goes black. The Pinball Fantasies menu also looses the sync while the tables' "icons" are visible, but is stable when the menu shows highscores or other texts and seems to be stable also while in game. So the sync problems seems to be happening depending on the content of screen.

Any tips how I could get those two to work better together or should I just try to find another used TV to my gaming setup? I think that the Indivision is fine as it works with those monitors and on the other hand TV is fine as such as it works with other devices, but there's some incompatibility between these two. Any settings that I could try to fiddle with?

TV has 4 HDMI inputs, I tested them all without difference. However I went through my HDMI cables and found one which seems to work almost without any issues at all, just one short sync break during the Pinball Fantasies menu and I left it running for quite some time. It is Deltaco branded HDMI-1020 2m cable, in case someone is interested.