You'll want the soil damp, but not wet, or you'll not get the penetration you're looking for. My 6 footer with ballast you see on it weights in the neighborhood of 1,000 lbs, and will take plugs out about 3" deep, when soil conditions are right. You'll probably Have to do some trial and error, according to soil moisture, to get the results you may want. Speed pulling it never seemed to be a factor on how deep it will cut the 2"-3" deep plugs. I have used it on my Ford 2000 with 3 spd aux. transmission, and have traveled at approx. 5-6 mph, and had the same basic results, as with the ole' IH 240 pictured, going maybe 3-1/2 mph. The Ford 2000's fuel consumption is twice what the 240 uses over the same amount of ground, and the ole' back won't take much of those bumps at 5-6 mph anymore either, so I go with the 240 now.
I don't know if Gypsum is available in your area, but you may want to check it out. I've read both pro's & Con's, on using it. If you have a County Extension Agent, you may want to contact them, and see what they have to say about it. It may have to be worked into the soil to work properly. I don't know if just some getting into the divots, or washing in after a rain, or just a topical application will be beneficial or not. One of the Con's, is that it can cause certain nutrients to leach away. I'm assuming your Houston Black has a high organic content. Again, if you have a County Extension Agent, that person would be your best bet for info, for the locale.
I did a quick look, and see Texas A&M has what looks to be a very diversified Extension Service, much like Ohio State has here in Ohio.
Texas A&M AgriLife Extension I didn't look into their site, but OSU has hundreds, if not thousands of what they call "fact sheets" with lots of info, that answered a lot of questions for me, when re-doing my hay field. Getting soil samples for possibly needed nutrients are near the top of the list, which we always did anyway. And your local Extension Agent should be more than happy to go over you with it, and make suggestions to help solve your problems. It's your tax money providing those services, might as well take advantage of it..!!