As long as you keep the buckles underneath that tarp you don't need the dripstrings at all.
I've spent many rainy nights in a hammock/tarp setup nearly identical to yours (your tarp is nicer, I had no doors) and never had an issue with water getting down the straps, past the buckle.
Changing the suspension to the hammock is going to be a trade off, I think.
Two things you're going to value greatly on your thru hike are:
- Quick setup
I think the buckles are better for 1 and a cord based suspension like the whoopie slings are better at 2. You're going to just have to figure out which you value more.