Was just at HF today and picked up a 212 for a snowblower. Anyway they had the 79cc, 212cc, 301cc, 420cc and the 670cc all in line. The 301 is pretty large compared to the 212, but the 212 is also wider than the old engine that kart came from, being a over head valve rather than a l-head (flathead). The benefit of the 420cc is, it's both pull start and electric start, so you could add a small 12v battery and have electric start. The 301 does not have electric start.
I'd vote for the 301cc or something of the equivalent in displacement. Not many engines are rated by the HP rating as Honda, Briggs, Tecumseh and other small gas engine manufacturers had a lawsuit against them about 10 years ago. All it would take to make a larger engine work is drilling out slots in the engine mount.
You'd want either a 1" TAV 30 or a 40 series. But you may have limited room for the larger engine because they are pretty wide and tall.