Glad my post was slightly helpful, glad to help, and thanks for the good words Mech.
I didn't know you had a belt in there, assumed it was similar to my Bayou 300 shaft drive (yes I assumed, bad idea!...:o) Yes it could very well be your belt, worn out, dirty from your missing hose, slipping, maybe the primary and driven pulley sheaves halves not moving or sticking with engine speed. Because before I knew you had a belt, I was going to suggest checking the clutch adjustment, as on my Bayou 300 if I use the wrong oil, dirty oil, or clutch out of adjustment, the engine will slip in top 5th gear when I'm going full speed, and almost sound like revving in neutral until I back off the throttle a little. Like you no problem in 1st gear, I believe roaring down the road in 5th gear is almost harder on the clutch than pulling 600lbs in 1st.
Doesn't sound to me like timing is an issue, if as you say the engine revs up normally and tops out, sounds more like a slipping clutch / belt issue. If you had shaft drive I could give you some tips on the clutches, but I know very little about ATV belts..:o)
Finally, about your starter, from what you say I think you have figured out your problem. I also had the same problem with my Bayou, starter would engage then skip and grind and not turn over the engine. Yes, drain the oil (or tilt it up 45 degrees on a block), take off the cover and pull the flywheel. Was not too bad, done lots of outboards before, though I did have to buy a special Kawasaki type flywheel puller bolt on eBay for $30 (not sure if you'd need it). It's called a sprag clutch, spins one way but grips the other. Turns out I didn't even replace the clutch, was still like new, just the tiny circular spring that went around the whole mess had stretched over the years and wasn't making the sprags grip properly. Just changed the spring and been good ever since.
Here is a exploded view for your ATV, I just love to pour over these so I can figure out what goes on inside a machine, might as well figure what's in there before you take it apart lol:
https://www.partzilla.com/catalog/kawasaki/atv/1997/prairie-400-4x4-kvf400-a1/starter-motor
You need the One Way clutch, 13194-1094. This is what you need:
https://www.ebay.ca/itm/196386773534
Or this, cheaper from China just use the spring:
https://www.ebay.ca/itm/395916084250
Reply to this post and you can get your manual.....:o)
Bellarmine