I've been playing with the TM as well. By others advice I switched from a 5x5 volume day to 3x5 for the last two weeks, and tho its too early to say much I think the results are better.
Your deadlifts stand out and are the only item I would take serious issue with. Going all out for a max would definitely affect my squats a couple days later.
I would also watch how you feel on the press and BP. I feel like I would have better luck gunning for a BP 5RM after doing a set of heavy squats than I would the press. If you stall quickly on the BP I would drop the volume/intensity on the press, or drop it all together and do some assistance work for your shoulders.
It's a lot of work but if you put in the effort (in your workouts AND recovery) I'm sure it will work for awhile.
it is my impression that the TM is a 3 day split. day 1 is a multi rep hi effort day. day 2 is a lower intensity a bit more volume, almost skill based work. day 3 is a max effort 1-3 rep test.
this looks like a 2 day split with twice a week work at varying intensities. and remember, if you change a proven program you are no longer doing a proven program. with the way you have changed it is not at all the TM.
if you want to lift 4 days a week and want to vary the intensity/volume look into 5/3/1. there are plenty of templates for accessory work to fit your goals and needs. to vary intensity over the week you can even do the 5 week on one exercise, with the 3 week on another, the 1 week on the 3rd, and a deload week on the 4th movement. i would recommend getting the book and allowing it to answer all your questions.
another option if you want more frequency is try sheiko. there are plenty of plans of i know there are threads that talk about how to order them as each one has a specific goal.
Man I hate to sound like I'm picking a fight but...
I don't think he's really asking if his template qualifies to be called a texas method (TM) program.
Yes it does things differently from TM. But the core idea of TM is manipulating volume and intensity and switching them up on different days to drive progress. His template follows that basic premise, so why not examine it and see if there are major problems.
It's cool you recommended a lot of stuff and I know you want to be helpful, but I am tired of the IT'S NOT THE PROGRAM camp shoving their cocks up people who decide to experiment for themselves. So sorry, this is not really just directed at your post, but a trend I'm tending to see.
Also OP I would watch for always opting to get 90% of a max. Be flexible and gauge your progress/condition.
why not just stick with the original template? adding more to the program most likely won't make gains any more likely or speed them up. in fact it will probably slow them down. if you want to do 4 days a week go for a more upper lower split. if you want to use TM try to keep it closer to the original. if you've never run it before at least try the original to get the feel for what its suppose to be like and do. then after a couple months start trying to make some more personal modifications.
Why don't you just run it and see how it goes? It's the only way to find out. Unless someone coincidentally did the same thing I don't think anyone can really tell you if this works or not.
But anyways, like others have already said if you haven't ran the original 3 day split version, you should. You can assess after progress slows and there will be less room for error when you decide to modify it.
I'll try to give some pointers on what I don't like personally ; Unless you come from a very low frequency/volume/intensity program prior to this template, having 5x5 would be a better idea than 3x5. This will allow you to "milk" the volume days to further adapt you for PR days. Then when the weights become too heavy to recover efficiently from, you can lower the Volume into 3x5. After you hit a wall once again with 3x5, you can change that 3x5 to ascending sets. The whole point of TM is to continually hit PRs on PR day. Volume days are meant to force adaptation for PR days. Light days are to keep you conditioned, so you don't only lift twice a week. However your template works a tad bit differently as you don't have "Volume, Light, PR days" but a mix of PR for one lift in a Volume day of another lift. The same concept works though.
Also, unless you've ran something similar to this before like Madcow, SS, or another TM template, maybe you should start with a lighter weight than just 90%. You will hit a wall really fast.