Been thinking of adding under deck bungies to my five year Outer Island. Could I just epoxy 1" webbing loops to the inside of the deck? Will this be strong enough?

Yes.
I've done this with 1/2" nylon tubular webbing in the past - just be sure to saturate the webbing with epoxy. It's a bit fussy to get neat loops and flat bonding areas.

Easier (IMO) and neater, though it adds a few steps to the process, is to make some 'padeyes' if you have glass (or CF) scraps around.

Stick the padeyes in place with thickened epoxy. Turn the boat upside-down to get gravity on your side.

You can make a 'mold' by taping a metal rod to a board with clear packing tape (even better is the red tape used to tape Tyvek and vapour barrier in construction). Lay your epoxied scraps over, cover with wax paper and press down with a couple of board scraps and weights. You will need 'a bunch' of layers in the layup to get something thick enough that it won't cut the bungies.
Trimming glass and especially CF is hard on wood-cutting bandsaw blades. You can hacksaw by hand. I bought a wet tile saw with a diamond blade ($49) for another project and it works well on jobs like this.

Make a bunch and give the extras away.....it puts scraps to work.