There is one difference that modifying won't make, and that is the aperture indexing post in the lens. I'm not sure how many cameras use this, but the F4 does, and it determines whether the lens can use matrix metering. I saw it identified as having to do with certain flashes as well, so it might influence how a dedicated flash operates on an F4. Anyway, the F4 will not matrix meter a lens without that post. It also senses the AIS slot, which I think is also ignored by newer digital SLR's, as well as at least some film ones (the F100 ignores both).
e.t.a. The FG-20 appears to have the internal lever for the AI post (it's down along the bottom), but nothing in the instructions suggests that it makes any difference to the camera. The FG-20 loses both the program mode and the TTL flash mode of the FG, so I wonder what, if anything, that lever does.