I don't believe that because that would mean the df1: drive and df2: drive are also broken. That would mean 3 drives having the same problem.
The CIA's are surface-mounted on an A1200, so yeah - you're still "screwed", unless you're REAL handy :-(
Have you tried different floppies? Perhaps you have a small batch that have been rendered useless due to magnetism, X-rays or something else? I was going to suggest looking at the tiny read/write switch inside the drive, but you now mentioned different external drives all having the same problem. Sounds like a mobo hardware problem then. Unfortunately, every chip is surface mounted on an A1200 besides the two Kickstarts.