FWIW, the skylight over my shower is fixed as well.
I want to muddy the waters a little on the epoxy v. rot discussion. I come at this from the perspective of having grown up with wooden boats and then designing and building fiberglass boats. Penetrating epoxies like Git Rot™ and Wood Rot™ are not as wonderful as their advertisers would have you believe. A better choice is good surface prep and a "structural" epoxy such as West System or even JBWeld. Stay away from the "table top" epoxies, simply because they are more expensive.
Epoxies are thermosetting polymers that come in two parts--a resin and a hardener. When you mix the two components in the correct ratio, a chemical reaction occurs, resulting in a very hard surface with high resistance to water, scratches, solvents, and many chemicals. That resistance is key. The solvents used to create penetrating epoxies leave the product much more porous so the small water molecule can easily penetrate them. Read that again. Penetrating epoxies allow more water to get to your wood than structural epoxies do.
Still, we want to get the epoxy itself to penetrate past the dry rot into solid wood. There are a couple of techniques. I recommend doing both. The first is to simply use extra slow hardener. The longer open time (you want 3-4 hours) allows the epoxy to soak in more. The second technique is to heat the wood before applying the epoxy. Get it a good 30-35°F hotter than ambient temp with a heat lamp or heat gun or hair dryer. As the wood heats up, the air inside the wood cells expands and outgasses. When the wood gets good and warm, turn off the heat source and apply the epoxy. The epoxy viscosity will drop (it will get runnier) as it hits the warm surface; you want that but watch for drips. Then as the wood cools, the cells will pull in the now-warmed epoxy with it.
As an aside, the heat is a balancing act. Heating the epoxy will shorten its open time. The epoxy reaction is exothermic so it heats up all by itself as it cures. Too much external heat or too fast a reaction will thin it too much so it runs out of your wooden part. It can also deform or even melt nearby thermoplastic parts.