And try a 240v -> 120 v adapter.
ONLY if it is UL-Listed. UL is the safety agency which writes the product safety rules and certifies equipment to be safe. Anything sold over-the-counter in reputable shops will be UL Listed.
Mail order bypasses the consumer safety agencies, and almost everything in the mail-order channels is dangerous cheap junk from you know where.
My first attempt at this didn't work. Originally, I capped one of the hots at the outlet and grounded the the other side to the bus bar. Swapped out the Circuit for a single pole 15amp, replaced the receptacle with a 15amp GFCI. And it fried the outlet after a few weeks.
OK, that should have worked. The issue was clearly workmanship problems in the work that you did. You should labor to improve your work quality until that thing works. We can help.
You absolutely should not be flying off in a totally different direction and trying new things, least of all with transformers, when you have not mastered the basics yet.
So to start, put up photos of the work done so far, relating to the breaker and the receptacle, and we'll try to figure out what went wrong.
I shut off the breaker, when I would flip it back on it would spark!
Might be a heavy load on the circuit (from a gas range? Unlikely) or it might be a workmanship problem. The photos will tell and then we can guide you.
How would you solve this if you didn't want to run new cable? (I have no problem changing the breaker/receptacle)
I would sit at my desk and pigtail black, white, bare wires onto a 120V receptacle. Then I'd crawl down to the socket and use big red or tan wire nuts, and splice those #12 wires to the matching #6 wires coming out of the wall. I would cap off red.
If I did not have a ground wire, well, I'd have to see what you do have. You might have ground after all. If not, it can be retrofitted.
Then down at the breaker panel, I would swap out the 50A breaker for a 20A 2-pole breaker or dual 20A singles. Why? To fill the empty hole. Can't leave a gaping hole in your panel!
Then I would cap off and insulate red in the panel, place black on the breaker, white to neutral bar and bare to ground bar. (which is sometimes the neutral bar, when in Rome do as the last guy did).
Considering the 6 guage wire, Can I replace the outlet with a 240v 15amp and then use the 240v --> 120v 15amp adapter?
No, all that money on receptacle and adapter would be totally wasted. Figure out why the 120V receptacle did not work.
Even more than that, I have a funny feeling you might not have a proper ground wire. That is not the cause of it not working, but it would make it illegal and dangerous to stick the socket you picked, a NEMA 14-50, there. NEMA 14-50 requires a ground. (or a costly 2-pole GFCI breaker and a "No Equipment Ground" label at the socket).
Is that risker since the thicker wire supports higher current?
No, that's not a risk. The risk is in the quality of work issues you are running into. We will work on those.
Should I keep the double pole 60amp circut or a lower amp circuit since the adapter supports 120v 15amps to be plugged into it.
Should I use 240v 50amp receptacle w/ a 60amp double pole?
If you insist on fitting a 50A "NEMA 14-50" receptacle, then it is mandatory to use a 40A or 50A breaker with that. NEC 210.21.
I hope I have talked you of dangerous mail-order adapters. If the adapter is stamped "UL Listed" with a file number, then it will have an internal fuse molded into the adapter (not replaceable) and that takes care of safety for the 15A outlet. UL requires that.
You better get your wiring right and sort out any problems with the appliance, because that fuse is NOT replaceable.