Tarptents vary quite a bit, just like tents do. Many of them are wind worthy, while others are not. Tarp tents are just single walled tents. They have many of the advantages, and disadvantages, of double walled tents. The main disadvantage of a single walled tent over a double walled tent is that managing condensation is more difficult. Other than that, the issues are pretty much the same.
Some tarptents are free standing, others are not. Even with a free standing tent, you have to secure it. If you don't put in the stakes, the tent will fly away. From a stake perspective, though, one advantage of the free standing tent is that if only one stake is poorly set, it probably doesn't matter. With a non-free standing tent, it may tip over if only one stake comes loose. There are a lot of outstanding ultralight folks in your neck of the woods and I'm sure they have a lot of experience with pounding stakes. That almost deserves it's own forum topic ("Using stakes in tough Texas dirt"). Depending on how many people respond to this post, you might split this into the above topic and perhaps "Wind Worthy Tarp Tents" and see what you get.
I don't think the slope issue is a very big one, assuming you have a good tarp tent. Even with a tarp, I'm sure there are lots of things you can do to reduce or eliminate drafts (the one big advantage of a tarp is that you have complete flexibility -- set it up high when the weather is nice, or set it low when it isn't). Personally, I'm not a tarp guy, as I typically camp during bug season. I am, however, completely sold on tarp tents (call them single walled tents if you want). The slope issue (and bumpy ground in general) is more of an issue with the sleeping pad. Lots of people love inflatables, despite their generally higher weight (over closed cell foam), because they can handle a few bumps on the ground.
What is the link to the guy who doesn't like tarp tents? I'm curious, as I've read some silly comments made by people on YouTube.