If you are talking about a Catalina 27, it's a deck stepped mast (I believe)... downing the mast and inspecting the mast step (where the real problem is) is likely your only choice. I know on my Capri 25, the mast step was bolted through the roof, into a metal plate glassed into the fiberglass. 12x12" or something. This is definitely the case on my S2.
I know 2 members of our club (with Cat 27s) had changed the flanged mast step out for a hinged mast step (to make it easier to self raise the mast), as our lake doesn't have any marinas with a mast crane. They stepped their mast themselves. Also the C27 is different in which the preferred mast raising is from a "tilted forward" position, so one would drop forward...
This isn't the end of the world, but it IS a decent amount of work. If you can do the work from below, it'll prevent the deck from losing the look. This work has been done on my S2 7.9 because it had a similar problem. They did the work from above, and painted a large section under the base... it still looks OK. My vote is if you don't want perfect LOOK (but it could be even if you painted the whole roof), work from above it'll be easier.
I hope others chime in, because I am not sure how much wood is in the sandwich on a C27. If you had that much bulkhead rot I'm not sure how bad the rot will be by the chainplates.
If you are OK with doing a decent amount of work, most of this is pretty straightforward, just keep in mind the mast step needs to be "exactly" the correct height when done... but if you keep the sandwich the same build height, that should be doable without a degree in advanced math (most use a 2x4 on edge and check for level over 18 inches or so both directions).
While it's raining I'd be noting each location of leaks.. Most likely locations are, chainplates, mast step, stanchions, and genoa tracks. Other places that could leak, winches and practically any other load based bolt through on the boat, rope clutches, cleats, etc.
Good luck and I hope you have some time to do a little elbow grease.
I know of probably 5 boats in our club (all different makes) where the owners have had to do this work. I still consider their boats "in great shape" and "well maintained."