Maybe it would be worth a try to get that interlace mode enabled?
I tried it again and actually the original IS interlaced on my TV, even if the timing is off-spec:
This is a picture of the PAL60 hack from the link posted earlier, which had scanline count and VSYNC timing adjusted to have an atari-standard progressive 262 line signal. I turned down brightness to make scanlines more evident on camera:
This is a picture of the original NTSC version on the same TV with same settings (wrong colors, because the console and TV are PAL). Note that there aren't visible gaps between scanlines, because every other frame is shifted half scanline down. You can see a slight flicker by looking close at the screen, but obviously that doesn't show on camera.
The TV I'm using is quite tolerant regarding the timing of VSYNC to generate an interlaced signal. But older sets (like a 10" B&W one I have) are much more picky. So results with Tapper might vary depending on the TV set. (The uneven line count in different fields, for example, cause the spacing between scanlines to be different in that old TV, so that alignment between the fields isn't constant from top to bottom of the screen)
A while ago I did some experiments on the subject, using different TV sets and with a logic analyzer connected to the TIA outputs to monitor the exact timing of the SYNC signals depending on the cycle the register are strobed. I quickly lost interest, but maybe I'll take a look again and post the results in a new thread.