first question at this site. Hoping to get advice. Like many others, I am trying to learn how to service my bike, but when you get stuck.... I used a strap wrench and a cassette tool and I managed to get the lock ring off the rear wheel setup. I thought everything would just "come off", but the sprocket is jammed tightly onto the hub. I feel like I need to rotate it counter-clockwise to get it off, but then the freewheel just turns. Not sure what to do next, suggestions are welcomed.
It's probably stuck because it's digging in to the freehub body splines.
Install just the lockring without any spacers. Use your cassette lockring tool to immobilize the freehub from turning, and use the strap wrench on the cog to lightly get it freed from the indentations. You hopefully don't have to apply so much force that the lockring gets torqued down beyond what can be undone afterward by simply grasping the freehub by hand, but if you do, just move the cog down a bit on to a fresh area and do the same thing in the other direction. (The indenting takes a long time to happen, so there shouldn't be a chicken and egg problem here.)
If you get it off and find the hub is chewed up, the other question is whether anything can be done about that. It's nothing you did wrong, but it's not necessarily a problem you can ignore because Gates cogs have been known to sheer all the way through. I don't believe that Gates makes cogs for Hyperglide that differ in thickness to be more appropriate for aluminum freehub bodies. (The basic problem is that aluminum freehub bodies can be problematic at the best of times and when it's one spot bearing all the load all the time, they sometimes get destroyed.) Some hub makers do produce freehub bodies that have interchangeable form factors in steel versus aluminum. Also a couple of the major OE type hub manufacturers also do aluminum freehubs with steel face inserts that can interchange with their regular aluminum ones, the catch here being that figuring out whether this is applicable and then actually getting the part can veer into advanced topic territory.
Don't compromise chainline doing spacer tricks to get the cog to an un-messed-up spot. Gates will have other problems if chainline isn't dialed.
It could also just be a really tight fit, or a tight fit that's getting stuck on the small burr raised up by indenting into the splines slightly even after being rotated back. If it's just tight you can probably walk it off by wiggling in one spot, then go 180 degrees away and wiggle up, etc. If you have to take down the burr, the preferred tool would be a small, fine safe-side square or flat file, but you could probably do it carefully with sandpaper too.
The Gates sprocket removal tool is the best way to remove the sprocket.
Here's a link to a short video on how to use the tool.
Do you own a chain whip? If so you can put an old sprocket from a cassette on the freehub, hold it forwards with the chain whip and gently knock the gates sprocket in the reverse direction with a rubber mallet or similar. it generally doesn't take much force to loosen these off an alloy freehub. If it has bitten in very badly you may wish to employ the gates whip tool in the reverse direction, if funds allow.