Yeah, without doors and parallel to the wind, the setup can become a "wind-tunnel testing ground". My experience was this ... At Pirate's Cove in the B.C. Gulf Islands area (east of Ladysmith). The tent was set up with the tarp broadside to the wind. And in porch mode (the side the wind was hitting was up a bit, like an awning). Because I hadn't paid attention to drainage, a small swimming pool was forming in the tarp extending out from the hammock. When nature encouraged me to get up at night, my head brushed under the swell of water, tipping it off the tarp, onto my shoes. When I returned to the hammock, I took the tarp out of porch mode and anchored the edge to the guy-stakes. The wind blew the tarp against the hammock for the rest of the night.
The next day, I reoriented the hammock so it was as parallel to the wind as I could make it. I realized that though, as humans, we have a tendency to see things level, there's no reason why the tarp ridgeline has to be level. So I raised one end (not one "edge" as it porch mode), creating a natural drain/runoff for water. The support trees added some wind blockage and the smaller doors on the WB Thunderfly helped too. Note that I most always use an under-quilt protector (UQP) for even more wind blockage. I did notice that when the wind moved over (not into), the tarp sides, it gave them lift, away from the hammock, instead of in. So the third night I angled the tent stakes a bit more, make them more "lift" proof.
Your 10 x 10 tarp is wide enough, and because an 11-foot hammock is ideally hung with ends about 10 feet apart, your tarp just covers the hammock ends. But, yeah, with no doors and blowing rain it can be tough. If it were a strong wind, and my tarp didn't have doors, I'd be inclined to set up broadside and close to the ground. But I'd spend more time assessing my site choices. More that once, I've had to move from my "View spot" to a place further down a slope so I'd be more protected from the elements.
I'm going to make your SuperFly consideration a bit more complicated

I don't know about 12-ft but I'm pretty sure you'll have an 11-ft and 13-ft option.
The minus for the 13-ft option is more cost, more bulk, and more weight. But the big plus is, if you decide to move to, or use for a few nights, a bridge hammock, you'll want the 13-ft model so it will completely cover the apex where the suspension dogbones come together. Also, I think all those "more" issues are only a little more. And the 13-ft model will give you more dry space outside the hammock.
But I guess another downside is that the 13-ft model needs trees further apart. So you see, it depends on where you normally adventure and the style/density of trees you'll have for support, and if you'll be using a "portable tree" like the TensaOutdoor Solo pole.
A "no additional gear" solution would be to snap your rain jacket on the tarp end as an additional (or only) wind block.