Welcome to mamapedia!!
Your son is not ready for potty training. It really should take months. I know for some it does, however, it should take about one week for day time potty training.
Night time training is TOTALLY different and will be done when his body is ready to dry all night.
IF you have cut back on fluids and he's still saturating and leaking a Night time Pull up? You might need to talk to his pediatrician to find out if there is a problem with his bladder.
You don't state your definition of "limiting" drinks prior to bed time -
what is his bed time?
how much does he drink during the day?
Are you SURE he's not drinking before bed?
You might need to use a diaper and a pull up to keep him from leaking.
I wish I had more information for you.