Just made a VERY interesting discovery. The flickering lines do NOT happen when hooked to a CRT TV... in PAL or NTSC mode. I have no clue how I managed to get this TV to view PAL, but it is. Of course, it's stretched past the screen due to PAL being a bigger resolution, but it's working. It's a JCPenney branded NEC from 1984... a nicely optioned model, too.
So if the flickering lines only happen on the LCD TVs, that just means that both of the LCD TVs can't natively support the 15khz video from the Amiga?
If I am not mistaken, what makes it even more odd is that my NTSC A500 doesn't get the lines on the same TV playing the same game.
Both LCDs support PAL and NTSC.
If it's stretched past the bottom of the screen, it's not really viewing it in PAL. It's just that the TV is able to sync to 50Hz screenmodes. You don't think actual European PAL TV's from that era had 25% of the image displayed off the bottom of the screen, right?
I implore you, get your system recapped and plug in an Indivision, especially since you're using LCD TV's. Yes, there are probably other ways of solving your problem (that are guaranteed to involve time, head-scratching, and many forum questions), but if doing these two things doesn't solve your problem 100% I'll eat my hat.