It can be done in the light.
I don't know what kind of reels you've got but may be able to put the strips in place without taping.
When rebleaching or refixing is necessary you just "skip the developer" and "do the rest" of the process.
Bleach sets the film up for fixing, they are interdependent processes, and the stabalizer/rinse is then naturally required to finish.
Some extra time in these chems, on the original run or as you plan here, is just fine because these processes unlike the developer are supposed go to completion.
The developer is the only bath that has to be timed to exactly the proper time.