Hi!
I have struggled with Amiga 1200 at some point in time with similar video problems, only vaguely remember to have solved the issue by changing that Sony chip you mentioned. Anyway as for question about that PSU, yes it will affect video output too. I have one PSU brick which does quite blurry image with any Amiga I connect to it. You might try and modify some PC PSU to work with Amiga to rule one out? Anyway good luck with troubleshooting your miggy!
Check this site out! Have been very helpful with my HW repairs.
http://www.amigapcb.org/
