Andrew,
I presume these are the ground pulleys which are fitted in pairs to guide the rope where it comes off the wheel. In engineering terms it is a low speed, low stress application, so a sympathetic low-tech solution would be appropriate.
Nylon tends to absorb water and swell in damp conditions (and as a former steeple keeper I know all about damp towers). You might consider using delrin/acetal for your bearings instead of using nylon. Acetal turns beautifully.
Can you turn the bearings with a flange on one side, then recess the flange into the pulley? A couple of countersunk screws, brass of course, through the flange would keep the bearing in place.
I would not use use metal or epoxy on a wooden pulley as they cannot move with the natural expansion and contraction of the wood. My initial idea would be to cut two shallow stopped grooves across the face of the pulley at right angles to the grain, then glue in strips of good quality plywood with a waterproof wood glue. Put a small woodscrew or a pin at each end for added security if you don't trust the glue. It would be wise to do both sides to keep any stresses balanced.
I hope they have offered to do the removal and installation for you!
George
P.S. Ha! Larry, KWIL and Mike type faster than I do!
Edited By Georgineer on 08/07/2018 11:06:46