I also live in Texas and learned years ago to protect my vent covers and skylights with horse stall rubber mats. You can find them at Tractor Supply. When we are finished camping for the year, along with winterizing the RV, I put my horse stall rubber mats over each of my skylights and vent covers so I don't have to worry about hail storms in the spring. The mats are made from a heavy rubber and I've never had one blow off even with 75 mph winds. When I remove them in late spring, I roll each one up and secure with with heavy duty Velcro tape to keep them rolled up. These mats are heavy to climb a ladder with, but it's much easier to do and less expensive than replacing your skylights every few years.
What type of lap sealant did you use between the new skylight and the roof?. Was it the same as the self-leveling you put on top of the skylight and screwheads after installation?
If my memory serves me correctly, it took right at one tube for the skylight. I always try to have extra lap sealant though so you might have two on hand just in case.