Well I fella I was talking to about these bikes works on scooters a lot, apparently he found a match for one of the parts or maybe both with something designed for pulling parts in a type of scooter, I just never got those details, never needed them.
Unfortunately I don't even know what to tell a web trawler to look for to even begin a thorough search. But it does exist nonetheless, other than hard dimensions (which are unlikely to be written in descriptions of tools like these, rather just described as which vehicle it's applicable to) there's not too much to go by, maybe gear puller or something of that nature in the scooter world related texts.
Be realistic, these are cheap things, order one from a good vendor, since good engine kits will come with (hopefully) equally good puller tools. I've stripped one or 2 but even then one was recoverable even after tossing it against a nice concrete and stone wall. I simply ground it down on a belt sander past the ripped threads and very carefully touched it up with a small file on the last thread, it worked just fine again.
The most mostMOST important part is to make sure the threads are clean on both parts before attempting to thread and to lubricate with a light oil, wd-40 is perfect, lubes and cooks off later and is a solvent so gook in the threads breaks up for threading. Just thread it in and back out lightly and then thread further, you really want several threads engaged to prevent stripping in the first place, ideally at least 4 FULL turns will give enough thread to be within the 'bounds' of the physics behind whether or not threads will rip out, but really as far as it will let you go is best. You can't be cross threaded even a bit, this is why I like wd40 because it makes the gunk loose enough you can feel with your fingers if it's thread catching thread or just something in the threads hindering movement, so cleaning with wd and a toothbrush greatly helps the chances you won't mess up. This goes with anything you screw in to pull a part out with, really, and well.
Bicycle_motor_works on eBay is a good go to, I'd trust a tool from him. Your tool may be salvageable at this point if you haven't burned it for being difficult towards you. Just give it a shot, you've already marked it as ruined at this point, no harm if it doesn't pan out.
I was just looking at some stuff from bicycle motor works bought the 40mm reed valve from them. On my puller it was so stripped I don't think I could make it work it would just spin and not grab. I got off the clutch and the drive gear with it but it stopped working on that sprocket. Still need a few of the bolts for the crankcase. I wish I knew a good quality metric bolt supplier. need about 8 bolts not including the clutch and magneto cover bolts and the bottom crankcase bolt. need the longer one for the sprocket cover too.
There are also claw type gear/sprocket pullers so you don't necessarily have to have any threads on the sprocket at all. The smallest ones can cost as little as a fiver.
I would rather have the thread in type though so it is small enough to be carried in my toolbag in case the sprocket woodruff key breaks during a ride. Also because I filled the space around the sprocket with epoxy so I can't use the claw type.
It was one of those trying too hard situations, they happen. I remember trying to pull an alternator out of a ford focus, it was cold and after getting numb hands and really pissed off for the good part of half an hour, it just wouldn't fit through!!
I went inside and had a glass of Tullamore Dew, came back out and it just came out with no struggle in about 3 seconds. Really couldn't explain what the problem was other than I forgot to start drinking before working on a ford.