I have had great luck with the Schwalbe Marathon plus tires. Very tough,you can feel the heft when you go to mount them.Very thick tough rubber,they roll with ease too.
Those Treks were also used for touring,which could explain the narrow rims. You can get 26" tires for them down to 1.125" maybe narrower. Those tires are in the 90- 100 PSI range,hence the Presta valve.
They are the correct rims,many of the better MTB 26" rims will have presta valves. Depending on the rim you should have no problem drilling them. Can you post a pic of the valve hole ?