If that 1000 has been sitting for a while, the rings may be stuck to the pistons. The general consensus around here is to pull the plugs , squirt some high grade pentrating oil or Marvel Mystery Oil into the cylinders and rotate the engine. Repeat 2-3 times over a week.
Get your valves adjusted in the meantime. Check BassCliffs site for the zip tie method if you don't have the shim tool. Get a spreadsheet from Steve
Then, start it up and ride it a few hundred Ks and check the compression again. This often frees the rings and brings compression back up.
While you are essentially correct in thinking an air cooled engine may have worn pistons or bores at that mileage, experience has shown us that lack of valve adjustments tends to burn the valves, because they are no longer closing. This fakes you out because you've put oil in the bores without changing compression. Well, having a valve open gives you the same result.
So, start with what I suggested because it's cheap, like under $50 (because you'll probably need a new valve cover gasket)
If that doesn't work, then you'll have to tear it down and measure. A full oversize piston set, boring, gaskets, valve job and etc will run about $1,500 or so. Many people find that not to be feasable, financially speaking
If you're lucky, some valves are burned and you can do a valve job and refurb for less than a 1/3rd of the above. You'll find the OEM oversize (if you can find them) are waaaay more expensive than the Wiseco kit
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