When I was in FL and still going to school, ie no kids, I played twice a week year 'round and got down to an 8 handicap. I haven't touched my sticks in two years, and it's been 5 since I played regularly. Getting a smooth putting stroke is all about practice, and the 10 minutes you spend on the putting green before your round, if you even do that, isn't enough. I'd suggest killing time by putting in your living room (if it's got carpet). You don't need a cup. Put a quarter on the floor, or try to hit a table leg. Everyone's stroke is different in terms of what they feel comfortable with. For me, a slow take away produced a more steady approach to the ball. For some, a short take away and acceleration through the ball produces better results. It's all about what you feel comfortable with.
I've got to say, I'm looking forward to hitting the range once I get done with stuff at the house. In FL, the soil is so sandy and usually soft from the constant rain that you'd get no roll on your drive. At least, I wouldn't because I generate a lot of clubhead speed, thus more backspin and loft. I'd carry 285 on average with my driver and sometimes the ball would check in the fairway. From what I've heard about Texas golf, the fairways are hard and you get prodigious roll. Giddy up.