Sorry, don't know your mechanical knowledge, so apologies if I'm over simplifying.
Those engines have the old points and condenser (capacitor) setup. These are behind the flywheel, which needs to be taken off to check/adjust. It sounds like you've been checking the magnet/coil distance which is not the same. If you want to keep the machine, I'd advise taking the coil/points/condenser setup out completely, and instead using the the electronic ignition from a Briggs and Stratton lawnmower engine. You will have a machine that needs less rotational speed to produce a bigger spark (especially noticeable when starting), which doesn't ever (usually) go out of adjustment, so is maintenance free. (second hand part is fine, and not expensive). There is a quick and dirty way to do this which just involves replacing the coil but I would encourage you to do a proper job and take the flywheel off.
You don't really need special tools to get to the points, but you have to go easy because you'll be dealing with (hitting!) aluminium (on the recoil unit) and cast iron (on the flywheel), not the most forgiving of materials.
While you've got the flywheel off, check that the flywheel hasn't moved from its proper position on the shaft (which will affect your spark timing)... The cutout groove on the main shaft and the cutout groove on the inside of the flywheel shaft have a small sacrificial soft metal bar (flywheel key) which locks them together. This should be undamaged and both grooves it fits in should be undamaged. If there is damage it's a faff but repairable (usually). Just means someone hit something hard while rotovating and that little bar took the damage, as it's supposed to do.
If your checking your spark by earthing the spark plug, try with the bare wire instead, resistance on spark plugs builds up over time.
Having said all of that, If I was doing it, the first thing I'd do is take the head off and see if there is any heavy scoring on the cylinder walls.If so, you will either have to spend money remedying it, or live with a poorly performing machine.
I've done this to a couple of these, so if you need more just let me know. There were quite a few videos on YT of what you need to do. Good luck!