Sigh. That's the problem with answering questions with "no, it can't be done." They come right back wanting a different answer. So, we went back to the Internet and searched on "preventing suckers on live oaks" and guess what we got? One of our own previous answers from 3 years ago, saying basically the same thing we did on this one.

So, we continued to search the Internet for the magic potion that solves this problem without work, and found an article from the Bryan-College Station Eagle, written by Neil Sperry. To quote the relevant portion of that article:

"Use sharpshooter spade to battle live oak suckers

Dear Neil: What can I do to get rid of live oak suckers that are coming up by the hundreds beneath my tree?

A: That's a fault of probably 10 or 15 percent of our live oaks. They vary genetically, and those sprouts are tethered to "mama." Your best bet is to use a sharpshooter spade and angle your cut so that you remove the sprout and as much of its small trunk as you can. You might consider laying a solid vinyl root barrier such as pond liner down over the area after you have removed them, then putting some type of decorative river rock or other heavy mulch to conceal it. Try it on a small area to see how well it works for you. Short of replacing the tree, there just isn't much more you can do."

Frankly, we wouldn't be too thrilled with putting a pond liner over the roots of your trees, because those roots need oxygen and water, too, but maybe it's worth a try. According to Mr. Sperry, it is apparently the variety of live oak that you have that is to blame, which we hadn't heard before, but it makes sense. As we said in the first reply, you can rake up and remove acorns as soon as they fall to avoid the seedlings, but we know of nothing and could find nothing in our research that will inhibit the suckers without harming the tree. As for preventing the leaves, if you remove the sucker so it doesn't create leaves to nourish itself, new suckers will have to continue to depend on the original tree root (which is the sucker's root, too) for nourishment. 

Moral: Having live oaks in Texas is wonderful, but not without price.