Oh dear- what you have is definitely why I never liked wide balsa stringers- they soak up water like a bricked camel and this is precisely what happens. Balsa in its natural, in-the-tree state is something over 50% water, and you might say it really, REALLY wants to be that way again.
Now, personally I will have nothing to do with any WEST product, lots of very good epoxies out there for this purpose and you don’t need to pay their WEST ripoff premium prices. System Three, for instance, makes their Clear Coat resin for this sort of thing and there are lots and lots of others. And here’s how I would approach the problem;
You will need some strips of 1/4 inch plywood, call them 4" wide by the length of the rot plus some length for ‘just in case you find more rot inside’, a plunge router with a collar ( as is used with jigs and such - Ryobi makes a cheap one that’s more than adequate for this and any woodworkers store has the collars ) and a hot glue gun and lots of glue sticks.
Carefully mark out alongside the stringer on the bottom, offsetting for dimension A above. Use hot glue to stick your ply strips down, go a little nuts with it, you don’t want those puppies to move. And it might not be a really bad idea to go maybe 1/8 oversize on width. That’ll get rid of the old stringer glue as well, which is probably Pretty Ugly by now.
Now comes the tedious part. With many passes and slowly increasing the depth, rout out the rotted wood and go fairly well into good wood, cutting through the glass too. Note that I show the router bit not going all the way to the bottom - you will want to scrape out the last of the rotted balsa with a narrow paint scraper and watch out for the sharp edges of the glass you just cut. If the rot doesn’t go all the way, then taper the end with a sharp chisel so you can make it look good where new and old meet. I don’t think you can save the old glass, plus it’ll look like hell on top of that nice new wood.
Pop the ply strips with a putty knife, don’t worry about hot glue residue just yet. Put in your balsa, ripped to the right thickness and as close to the nose-tail deck curve for that section as you can come plus some extra thickness for planing - whatever you’re comfortable with, slightly rounded on the deck side ( a light sander and coarse paper is a good way to go for this) . Bed it in epoxy, use plenty. Remember that the balsa will soak up epoxy almost as well as it’ll soak up water.
Okay, I’d then use a belt sander to take down the balsa to ‘close’, one of the few uses for a belt sander anyplace near a surfboard. Finish with a random orbital sander, taking off the hot glue and excess epoxy as well. Glass a strip on to bridge the gap - I’d use a couple layers of 10 oz Volan, the first maybe 4" and the second at 6-8" wide, the edges of both layers well feathered with the sander - hotcoat,sand, gloss and go surfin.
Oh, before it slips my mind:
Now that you have your nifty new plunge router, and as you got rid of the old fin sometime in the process, I’d rout in a nice new Fins Unlimited/Bahne box in your new wood rather than trying to re-use the old fin in some way. Same deal about making a fin-box routing jig as with the strips above, it wants to be oversize by dimension A in all directions, so that it’ll fit the fin box nice and snug
leastwise, that’s the way I’d tackle it…
hope that’s of use