It turns over really slow, then stops and smokes, new solenoid, starter was tested and I was told its ok.

step 1 failure.(the act of)
pull the starter small wire log off the starter,solenoid on side of starter motor
see problem gone../ if yes the starter relay is stuck closed and bad. (happens) or short to the relay coil same.(the volt meter finds it)

motor stuck, last line, and crank shaft did not turn?
and motor now spins up super fast RPM and engine does not crank.???? that, yes seen it.

your post is not clear at all, 1/2 way told. for sure.
first off we can not hear it or see it spin. any of it.
"constantly engaging the ring gear" (key off? and you hear the starter spin and crank shaft spins too)
not told clear enough to the blind and deaf. sorry !!!
I have seen them all (fails) and fixed them all.
even back in 1960s with starter shims and all that.
(three cheers, shim days are gone !!!)
oK>? nothing new here for me,.just me blind and deaf.

the new starter fits to a precision bell mount that is not loose and never ever needs shims.
the ring gear must not be a wreck or bent. ever.
or ring gear stripped out or mangled, teeth.

if mangled the pinon sure can get stuck.
if the starter sticks on(spins) key off, pull the small wire to it.
the starter must stop, dead. or see why below.
if not the solenoid is jammed, and on new starter that means the ring gear is a WRECK, stuck pinon out.
a stuck solenoid causes the huge contractor inside it to close and key switch does nothing at all (off)
that means it is pure mechanical failure
pull tranny bell lower inspection cover (hope it is there)
and turn engine and see ring gear damage or warped
or mangled ring. or teeth a mess.
this answer is for stock car
and this happened out of the blue
and did not buy a car failing like this, hacked up or with wrong parts here.
the man in the text box is blind, and deaf and can not know history here ,unless told.

the pull small wire trick solves the, is body wiring wrong or is it just starter failing only.
yes 2 man tests to pull battery neg lug see motor stop.
motor means DC starter motor that starts an engine
today with EV and Hybrids we all know the difference.
2 man test allows one guy to yankk off battery lug
and put it back OMG it keeps going even key off.
then repeats the test small wire pulled off solenoid next then battery lug back and IF starter is NOW silent (body wiring bad, or relay bad or further back)
starter keeps going proving the solenoid is jammped
for sure at ring.
4 starters are not bad it is jammed at the ring.

rule#1 keep battery charged at all test.
some cars with BCM and low battery can cause starter to activate, at 10vdc or less battery.

bad starter maybe. or solenoid solenoids are the typical problem with all gas powered riding mowers these days , not sure why no one can seem to make one that will last a whole season any more, I've replaced 6 of them on my craftsman in the last 2 years but yeah either starter or solenoid are what I would look at. could also be one of your safety switches not making properly but usually the solenoid is the issue. those Kawasaki motors are straight up work horses though and you can now run synthetic oil on them which means if you do they'll last you forever.

Idle air control valve or passages clogged partly . Your best bet , take it to a qualified repair shop.

Not the coil, wouldn't affect or be affected by the slow starter. I would double check grounds and battery, starter, and alternator connections for a clean tight connection. I would be looking at doing voltage drop tests to look for high resistance in the start circuit.
You may have to get under the dash and find the source of the smoke. Sometimes the back of the fuse panel where the wiring connects in will get so hot the plastic starts to melt. Then the wires and connections go bad, and you can even have current cross feeding into another circuit-like your wipers are doing. So I would pull off the fuse box and check for that. Keep looking for something that burned. It's got to be electrical.
Starter and solenoid being only 2 years old, should be good. But if starter to battery positive post has no high resistance in that connection, and battery ground is known good, and if the small (?purple?) wire to starter solenoid has battery voltage or very close to it, when checked with a voltmeter while the key was held in crank, then you might want to have the starter taken off and tested. The solenoid will be tested as well. If when you checked the small wire to solenoid with key in crank, and had much less than battery voltage, like 5 or 6 volts, then problem is in start circuit between the ignition switch and the starter solenoid.
Good luck. Let us know what you find out.

use jumper cables direct to the starter that will test the starter next jump power to the small wire on the solenoid that will test the solenoid next jumper the safety switches with a paper clip

Hello! I would suggest having a look at the Brown wire that connects to the starter solenoid...It may be touching chassis ground...Also check the Large Red lead that attaches to the starter...One or both are touching chassis ground...If the Red lead is against ground it will not blow a fuse, in that it is connected directly to battery...And give the systoms that you have...Guru...saailer

I’m happy to help further over the phone at https://www.6ya.com/expert/david_6df67de3b14de867

it is hard to say exactly what the problem is, but it sounds like the starter, starter solenoid, and or a charging problem. 1. last year I am assuming that the battery was low on charge and once you jumped it, it would start with the key for the rest of the season? if yes your battery should be OK just make sure at the end of the season you disconnect it and store it some where cool but not freezing. if you had to jump it all the time the battery and charging system has problems,(cables)(?). 2. if you have to use the car to jump the mower make sure the mower and car are both 12 volt systems, and the car should not be running. 3. make sure the battery is fully charged and there is no corrosion between the cables and connections. 4. once you do the above you can jump the solenoid to see if the starter is bad, if it moves it should be good, if you have to jump the solenoid make sure the mower is in neutral and the wheels are locked so it cant jump forward. also make sure all your safety switches are engaged, most mowers have switches on the seat, the blade engageing handle, and breaks.
The lights might have a bad connection at the battery, follow the wires from the lights for fuses and check them, some models have to be started before you can turn the switch back to turn the lights on.

did you use a new starter or a used one,if it was a used one it or the solenoid may have a problem if its a new one it still could be a bad new starter or solenoid(it happens).you may have a dirty ground where the starter bolts to the motor that the surface may need to be cleaned,or it may be dirty wire connections at the starter solenoid or connections not tight(?).i assume when you had the battery tested at the shop you didn`t have them perform a starter test.some times it can take several attempts to catch the starter acting up.

I had this problem last year. I was told by a reputable Yamaha service technician that I could "jump" the leads on the solenoid to unstick it. It worked. However, in retrospect, I wish I would have just replaced the solenoid, given that it is a relatively cheap component (~$40 new). Since then, I had the sticking and clicking problem again this past March right at the beginning of the season, and during my attempt to repeat the success, I shorted out the bike because I got careless about what my disconnected wires touched on the bike. Shame on me. So I'd recommend replacing the solenoid.

Sounds like a timing issue. If you have points set them to .018 and then static time the engine.
Hope you have that Shovelhead going by now.