I'd still have to pull out the floppy drive to route the cable, right?
Depends on how you route the cable. Some people just stick it straight out the back. Others remove the RF modulator and stick it there. IMHO on an A1200 this is the best solution. Even better if you can find one of those HDMI output connectors (attached picture, sorry, don't have time to grab a high res image).
Ymmv, I don't really consider moving the floppy drive to be "surgery". :lol: