Starter motor not turning and the alternator are 2 different things entirely. The truck will start and run without any alternator in it at all, and has zero effect on how well it starts.
The 200 amp alternator is still massive overkill for the power requirements of these trucks. Your standard car with all it's electronics will easily run on a 60 amp alternator at 12V, which is equivalent of 30 amps at 24V. All you need power for while running is operating the lights, transmission, keeping the fuel shut off solenoid open, and recharging the battery power used while cranking. The batteries handle the cranking. Size of alternator output will just affect how long it takes to recharge the batteries.
The larger alternators are mostly there in case auxiliary equipment gets installed later.
To me it sounds like you have a bad connection somewhere. It might be on the positive wire between the batteries and the starter, or it might be a loose connection on the ground cable side of things such as a loose bolt at the DC shunt in the battery box (I've seen multiple people say they had issues with those bolts being loose)
The regulator for the 100, 200, and 400 amp alternators is sealed and no adjustment possible.
Compare voltage output at the batteries and at the alternator output. They should be 100% identical. If they aren't, especially when you do things like turn on the aircon, then you have a bad connection somewhere that needs taken care of. Bad connections such as corroded connections, or loose connections making poor contact, are probably the main issue people have with the HMMWV electrical system.