I have a site, but you have to pay to play. The Legislature's site is also slow to update, but I don't think they let more than a year go by without updating. That might be the best you can do: www.capitol.state.tx.us.
I guess your inability to keep up with the law without expending money on a subscription site might be what keeps us attorneys in business. You might try your local library. I am not sure if they would have an updated copy of the Statutes. I know that the courthouse in Belton has the updates--that is if someone is bothering to update the books (it was a problem at one time). Probably your best bet would be to set up an arrangement with a local attorney who does some banking law--tell them that you would be willing to be a resource to them, i.e., answering compliance questions, if they would be willing to have someone on their staff occasionally check for updates to laws that you are researching--or better yet, let you use their library occasionally. I can't imagine that you would not be able to find an attorney willing to let you do this. Remember, however, many small firm attorneys have given up their paper library of statutes and rely on their subscription services. You might talk them into letting you use a spare computer occasionally (the only problem is they may pay by the search).
Sorry, this is so rambling--I am just thinking while I am typing. This is a problem.