The reason your having so much trouble mounting is because you bought a USED set of racekart tires.
The Beads and Sidewalls of brand new racekart slicks will stretch enough to easily mount on a rim by hand,
provided the installer is using some means of lubrication for the Beads to stretch over the rim..
Racekart tires harden over time & use, that's why it's not uncommon for the top drivers to replace their tires
every single week of competition, then they either throw away or sell off their old ones; even thought these tires
don't show any signs of wear at all.
To compound the issue, sometimes these used tires sit around hardening even more for years & years before
someone like you finally buys them... I've got a feeling that's the situation your dealing with now.
Most racekart shops have a tire installing machine that would force the bead over the rim, and would probably be
able to install, set the beads and inflate your used set of tires. Possibly for like only $20...