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...these are difficult to remove when they've been in place a long time...which is mot of them. This applies even using the correct, purpose built tool for removal. I cannot imagine trying to remove one using a homemade tool ground from a socket. What usually happens is that the wheel and freewheel assembly slips off the tool prongs, and this leads to damaging the either the tool prongs themselves, rounding the flats and corners, or damage to the removal slots themselves.
I presume that the "outer ring" you mention is the one that holds the freewheel cog mounting base to the freewheel body itself. You don't take that apart to remove the freewheel, and if you do, it is left hand threaded, not right hand like the mounting threads themselves that attach to the hub threads. What will happen if you do that is that all the little pawls, bearings, and springs will drop out, when you lift off the cogs. They will drop on the floor and hide under your workbench.
But if the slots for removal of the entire freewheel assembly are damaged enough, you'll never get it off except through destructive removal. Which is accomplished by doing exactly that, as described above, then using a bench vise to clamp the freewheel body, while you twist the wheel to remove the hub threads from the freewheel. There has to be at least one Youtube video that shows you what I mean, under "destructive removal of freewheel". That way, you at least save the hub and wheel assembly.
My first step in your situation would be to find and borrow or buy the genuine two prong removal tool for Suntour. And mix up a batch of 50/50 ATF and acetone, using it for a penetrating oil at the interface between the freewheel body and the hub threads. Many of these freewheels were origanlly mounted without using grease or anti-seize. So there's been some corrosive binding over the years of steel freewheel body to aluminum alloy hub threads. Sometimes they just cannot be salvaged.