Do you have an "intermediary" mac that has a LocalTalk port, or an ethernet interface for your Classic? If so, try a network install.

You could also try installing 7.0, then grab the appropriate extension from from 7.5.5. That will be many fewer floppies.

Another problem with those drives is dust, so it may just need a good cleaning. (The fans push air out of the case, which means air must flow in somewhere else. The floppy drive is one of the places that air can come into the system, to it tends to have a lot of dust coming in with that air.)