[caffel]

Look in the grainger catalog Grainger for shaft sleeves to fit inside the existing hole.
These are made to adapt say 5/8" shafts to 3/4" bores (other sizes too).
Choose the right size, then have a keyway pushed through the wheel hub. The shaft sleeve adds strength and has the keyway already in it so the key can protrude into the wheel hub. You may need to make the key yourself.
Note there are pneuamtic wheelchair wheels that are close to your dimensions and which have 5/8" or 3/4" axles.