1/8" balsa reinforced with cardstock (or just a thin layer of epoxy) will be plenty strong for an E45 as long as you use something like a long rooted delta, trapezoidal, or clipped delta shape (Asp, Nike, etc.) that doesn't hang way out there and lend itself to flappin in the wind. 3/16" balsa should survive naked, but if you want to reuse the rocket, a coating of something is needed to keep them from absorbing moisture if you land in wet grass, etc. These fin shapes that aren't swept back will also prevent or minimize landing damage and allow you to reuse the rockets without wasting time on repairs, assuming you find them.

Epoxy is fine to attach the fins, but if you are using regular hobby rocketry paper body tubes, plain old yellow wood glue will hold more than the wood or BT. No big deal unless you are epoxy sensitive. Jerry Irvine has noted that he's stress tested some wood glue assembled airframes with some pretty gnarly motors. I can't recall how large, but they went well beyond E range. I don't see a need to mount balsa through the wall. If you are using heavy airframes and fast descent rates you might go to 1/8" plywood TTW, but what's the point if you are losing most of them? lol

If you go the epoxy route, several batches of fins at a time, laminating a bunch of them at once on a table. Then install them on the rocket body at your convenience. Several choices are available, West Systems, Aeropoxy, Z-Poxy, and several others make slow cure hardeners or packages for laminating. West Systems is probably available at nearly every boat/marine shop. Just don't forget to get some quicker curing epoxy for attachment!

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I love sanding.