Another way to go would be an ENO doublenest hammock:
https://www.rei.com/product/754773/eno-doublenest-hammock

You can hold off on the accessories by using a waterproof tarp with grommets, bungee cords, and (four) stakes. https://smile.amazon.com/Outdoor-Products-Rolled-Tarp-Foot/dp/B00G242H22/ref=psdc_511396_t2_B07PZDWRQX.

I survived some very stormy nights with this setup.

As you're going in April, it's worth noting that it can still get quite chilly in the north Georgia mountains. You'll want some form of sleeping pad regardless of whether you're tenting or hammocking.

Though I don't know how the pandemic will impact through-hikers, the Georgia portion of the AT can be very busy in April. I wouldn't plan on staying inside a shelter.

I don't recall at exactly which point you are required to use a bear canister, but you can avoid having to use one if you plan your trip from Woody Gap to Neels Gap without an overnight. I have found bear canisters to be very effective - against mice.

I'll check on that.

Where have you tracked down Tyvek? Just leftover from construction sites would probably be the best bet?

Otherwise I was eyeing up this tarp from Amazon. It's a $4 add-on item, and it's 6'x8' and weighs 2.2oz. There's a 6x10 as well.

EDIT: Actually I see now that it's 9.5 oz. So if I had 2 of these, all of a sudden I'm 1.5lbs up.. yeah, seems like Tyvek would be nice.