800 ves losing spark on one cylinder

If bar warmers ground out to bars they don't work, all the current bypasses the heating element.

Do you have spark at both plugs? I've had Edge sleds with a bad coil give no spark and a little more work to diagnose was a bad stator. The stator is about all that's left (edit: spark-wise) from the sounds of your repair attempts. They have specific resistance values you can measure to test before throwing parts at the problem. Sorry, don't have those resistance values, but i found them on here several years ago.

I hope he at least tried changing plugs, but good idea to ask for sure Steve.

Voltage regulator is in the left footwell area.

Check spark, so you're not guessing it's a spark issue when it may infact be a fuel/other issue. The fact that it runs fine at higher RPM & load makes me think spark system is ok. The bad stator I dealt with wouldn't run at all and had no spark. The bad coil I dealt with ran on 1 cylinder but never cleared up at higher engine speed.

If the needle/seat isn't closing properly, I would expect to see gas pouring out the carb vent line into the airbox, though it might not be that extreme. Last fall I had an 03' with a good needle/seat but the O-ring that seals that assembly to the carb had gotten hard/dried out and no longer sealed. It poured fuel out the vent line when running, just like a bad needle/seat. O-rings are a lot cheaper though.

Have you cleaned the carbs? I would on a 14 year old used sled. Just note the position of the fuel & air scews (gently bottom them out, counting the turns required to do so & write the numbers down) before removal.

Clean the VES valves. While you're in there, make sure they're the updated SS valves (or titanium--less common) and not the aluminum ones (they break off and drop in the cylinder, destroying the engine). It may not be the case, but a valve stuck wide open could really kill bottom end response, though I doubt it would cause it to go so rich it didn't fire.

When you clean the carbs, check out the reeds. Makes sure they close all the way and they're not coming apart.

v force reeds back then were garbage. I would definitely check the reeds and make sure they are not broke, cracked or frayed. Broken reeds will cause a rich condition at idle that will cause what you are describing. If the reeds are good I would check what pilot jets are in it, You may have to drop them a couple sizes. I know that with reeds you have to drop 3 to 5 sizes on the main jets because it pulls so much more air it will naturally pull more fuel causing a rich condition. I had an 03 800 edge with twin pipes and when I put reeds I had to go from 420 mains to 390 mains to get it dialed in. The carburetors in 02 have a different needle than 03 so they will be jetted bigger stock (something to keep in mind). I would make sure you have spark with a new plug just grounding it to the head and pulling it over and then if you do start looking at reeds and pilot jets.

if it runs great off idle i would throw some new plugs in unless they look brand spankin new. oem champions too, not the ngks.
i would also pull the carbs and all the jets, note the sizes for future reference, blow through them, and reinstall. i check reed pedals every time i take carbs off. i never had v-force reeds but worked at a dealership back in the day and every sled i ran on the stand that had v-force had a high hanging idle. seemed lean to me.
02s were strong runners. i want to say different timing and jetting, but jetting for sure. scary lean mid-range compensated by fat main jets. i took mine to '03 jetting, got the egt temp down in mid-range, leaned out the mains, never seemed to run any stronger than stock all said n done though.
pull that plastic shelf in the airbox, the one before the carbs, not the top flat one. and the oil drenched foam.
but my initial thought was just throw some new plugs in, fill it with fresh premium and run it! might just need the cobwebs blown out