A poor connection will make the starter turn slowly under load, guaranteed. Additionally, that connection will get very hot. Have you noticed any melted insulation or smoke during one of these hard-start episodes? Venting the tank will have NO effect on starter speed, just in case you were wondering. A stuck vent with either pressure in the tank or a vacuum may cause hard starting and will certainly affect idle an may affect running. Our UXV 500i side-by-side is a real crappy, unpredictable starter. The starter will stall trying to get that big piston over dead center, sometimes. Other times, it spins everything to a fine start. Not predictable so we have to be ready with "pilot technique." Personally, I think the starter motor and/or battery are too small for the application. The DT300i starts the same way, EVERY TIME. The 500s seem to be the ones with this problem. One thing to consider is the field strength of that permanent magnet motor. There are places somewhere that can remagnetize those pole pieces. More field strength = more torque. Another "bright idea" may be to replace the cables from battery to starter with the next size larger. This would include to and from the solenoid. More current = more torque. Both of these "bright ideas" would be easier than adapting a geared starter to the engine. De dee could do that but he is in Canada!
Please regard all this is NOT experience with the 500's but based on experience with other machinery systems. Use a "grain of salt" when trying these ideas of mine! You will probably come up with other, better ideas. I have no doubt that this problem on this model will be solved by the people on THIS FORUM and no where else!
Karl