Brakes lock up after about five to ten minutes of driving

Sounds like you have a master cylinder issue but the hard pedal does point to a booster issue.

However, how do you know it is all four wheels that are locking up? Also, what do you have to do to get it to release?

https://www.2carpros.com/articles/how-to-replace-a-brake-master-cylinder

What I would do is get them to lock up again and then lift the vehicle off the ground to find which wheels are actually locked up.

https://www.2carpros.com/articles/jack-up-and-lift-your-car-safely

Clearly we need to be sure it is all wheels because that will change what this could be. I understand it may feel like all of them but it may not be all of them unless you have proven that a different way.

Let's start with this and go from there. Thanks

In the 3 days that it was "fixed" did you drive like normal and it operated the entire time with no issues?

If so, then was this the same issue that you replaced the booster for?

Did you just replace the booster or did you get an assembly with a new master cylinder as well?

See below for more detail.

What I suspect is happening depending on these questions, is the brake push rod is sticking and causing the brakes to drag.

You could try that but I suspect the rod in the master is where it is sticking so that means replacing the whole unit would need to be the solution.

I am not sure this will work but try getting it to lock up again and then push down and actually pull up on the brake pedal to see if they release quicker then before. I doubt it will be an instant thing but it may.