Good question. Pretty much everyone on this forum has experience with chainplates. You can do one at a time. If you are doing it with the mast
up you'll want to run your main halyard
over to the side of the deck
where you have released the turnbuckle and chainplate to keep the mast
from bending or falling. Attach the halyard
and take tension before you release anything.
You can readjust the rigging
once you get both sides completed. Google
tuning your rigging
or ask the question here again once you've completed the reinstall of your chain-plates. Use a sealant/adhesive that stays flexible. Boatlife polysulfide is pretty good. Maybe 3M 4200 would be ok.