I hear ya on putting in big miles on a bike that aint "proper" for long rides.

Are you riding only on pavement? If so I recommend 100% pure slick tires for improved grip and less rolling resistance. Treads are noisey and vibrate anyway. A high TPI count and supple sidewall will give you the ride you are looking for, but you'll pay for it. Totally worth it to me because the ride quality and experience are too important to me to cut corners.

Take a look at these and see what best suits your budget and weight requirements. None are cheap though.

Schwalbe "Kojak" 26 x 2.0 available in wire or folding bead, 70psi "max" Personal experience = excellent.

Freedom "Thick Slick" 26 x 2.0 available in wire or folding bead. 65psi "max" Personal experience = excellent.

Bontrager "Hank" 26 x 2.200 Wire bead only. 65 psi "max" Haven't tried these (yet) but the reviews are great and it's looks great too.

Kojak HS 385 | Schwalbe North America

Freedom Bicycle » ThickSlick

Bontrager: Hank (Model #02856)