Rob, the tailpieces are wood-screwed directly into the top, so you may have to do the dowel+glue workaround when you go to re-mount it. Be sure and use the right size Phiilips to turn those screws, as obviously, the screwdriver slipping and skittering across the top of the axe . . . . would ruin your day.
Unlike any other hardware on the axe, the tailpieces are clear-coated, so you'll have to get thru that finish to buff it out, and decide whether or not to re-shoot with clear before you put it back.
The bridges are riding on threaded studs, so you simply keep raising them in their mounts till they come free. Then you can dis-assemble them for maintenance as you wish. Along with every other brass bit except the tailpiece, they're not clear-coated and you can use your polish on the parts straight away.
I always advise the first time you do this to take some digital pics to remember which way it's facing, and also get an idea of where they saddles are sitting along their adjusting rods. If you dis-assemble them completely, you'll unscrew the saddles off them, and to speed up re-assembly, you'll know about where to return them. It's good to do this at new-strings time, and if they're roughly in place to begin with, it will save you time with the strobe tuner.
The first time I did this, I took the bridge completely apart, cleaned and lubed every thing, and put it back on the bass . . . . with the saddles facing backwards. So off it came, took it all apart again, re-seated the saddles properly and started over.
So some digital pics for their relative positions as well as the height the bridge was sitting at before you started will definitely save some time !
Joey