“The key is not to make any major improvement to the property after you have been locked in (an addition, ect).”
You are only locked in on school taxes. All the other many taxes can still increase. Been there, done that.
In Texas school district taxes are about half of all the property taxes you pay.
The city is about 1/4
so... if the city and school are locked in only the county and/or possibly a local community college part is the only part that could go up which is only 1/4 of the total.