dipper rods fail at high rpms because they have crappy lubrication properties. The gx620 is pressure lubed. You can safely turn them 5500 rpm no worries. As far as the head goes, just looking at the head alone, they look very VERY similiar to the gx340/gx390 heads, so Id say you could probably slap on some HD single rate springs, jet it a bit, get a high flow header (possibly weld it yourself), and youd have some good mods.
A lot of guys that run them on mini buggys use the comet 780 series torque converter. If you run a 40 series (esp the knock off version) you may end up chewing up your belts and have some issues with that much torque. Again, depends on what you are putting it on.
there are relatively new predator 670 performance parts coming out. Might want to give them a call about your 620, I know for a fact that the CAMSHAFT is the weak link here (e.g. plastic).