I will never forget my last night of a week long trip, using both a hammock and HHSS for the 1st time ever. And I have told it often to folks with problems like yours. The only trees I could find (at the spot my tenter friends wanted to camp) were oriented so that my little HH tarp was open on the foot end towards the lake a few steps away. The wind was howling off of that lake right into the foot end of my tarp, most of the night, and it was at least in the 40s if not colder. Turns out my buddies were having a chuckle about how I was going to freeze my butt off. Turned out I was the only warm person that night, my buddies were cold and miserable rolling down hill and dealing with rocks/roots. Once I got past the noise of my tarp flapping in the wind, I never even knew it was windy at all. Snug as a bug in a rug all night, one of the best nights sleep I ever had. I was a happy camper next morning, surrounded by grumpy folks who had a miserable night.
Anyway, IMHO, your best approach might be some sort of at least water resistant sock or under cover, whether a HHSS or 2Q UQP or something home made. Other than that, a tarp big enough to mostly close the ends.