When I first rented out my property, I had to prorate the deposit. The means I divided the deposit (which was first and last month's rent) into equal amounts over 3 months. The rent then was for $900/mo. That means the tenant paid an additional $600 a month instead of the initial $1800. You can, of course, divide that amount for a shorted period of time. That was the only way I was able to get a quality tenant.
I didn't know that about the Texas rental law, but that sounds fair. In my contracts for renting, I don't refund their deposit but so far I haven't had to do that.
Maybe doing a 6 mo lease would be best for you (at least worth a try) if 1 year isn't working out for you. Did the tenants say why they didn't want to stay for the whole year? I've had some friends not stay at their places because the landlord ignored them and refused to fix things and their neighbors where horrible.
Just some food for thought. I hope that helps some :)