Bristol may have changed masthead designs over the years (or you may have a different masthead box installed by a previous owner). The original masthead box is attached with thru-bolts that also fasten the main shroud mast tangs to the mast. It uses 3 ¼” bolts. It sounds like your masthead box is attached using tapped holes thru the mast wall and into the flange of the masthead box. If the box is closed, there probably isn’t a need to remove it from the mast. You can order new sheaves for the masthead and install them without removing the box unit. However, you may need to drill out the screws that are stripped to get your masthead box off. You might also try using an impact screw driver. (Undoubtedly, the stainless screws have corroded in the aluminum threads and seized. You can prevent this in the future by using a dab of latex house caulking on the threads as you screw them into the tapped hole. The caulking will also lock the screw in place.)
The wires for radio antenna and the masthead light(s) exit the mast below the masthead via holes. If you have no holes you can drill them. You can use a plumber’s fish wire or even a small diameter rigging wire (or some galvanized wire from Home Depot) to fish new wires thru the mast (remember to fish a separate set for the steaming light at the spreaders). You might also take this opportunity to run some PVC pipe down your mast to hold and protect the wires. Once you have all your wires in place, I would add a fish string of light strong line so that you can use it anytime in the future.
Masthead sheaves: measure the diameter of the center hole and the width. You can order new ones from Rigrite, from the folks at MetalMast (see above in this tread for contact info) or from Garhauer or others. The sheaves you have are most likely Bakealite (a popular material in the 60’s for sheaves). If they are chewed up it is probably from frayed halyard wire. They can be sanded to clean them up.
Some photos would be very helpful for me to be more specific.