What do you have to lose by submitting an article for publication? You'll have an even better record/credentialing/verification of the work you've put into it by being published in a Journal of good reputation. In the worst case, you will get a rejection letter, perhaps with a good explanation of why they are rejecting the article. The in-between case is pretty good too: you'll receive a referee report which may criticize your approach, suggest particular points to be polished and corrected, perhaps suggest a different approach to take, perhaps suggest that some of this work has been done by others who you shoud read and study or perhaps refer to in your work.

If you're lucky enough to be asked to rewrite and resubmit for consideration, you're possibly on your way to being published. If not, you'll at least have made some progress and educated yourself about the academic publication culture, and will be more prepared for the next article which you prepare for submission.

May I recommend that you find out what your activation energy level is, exceed it, and go ahead and clean up your paper and submit it for publication. Best wishes and good luck. Go for it!

Would you mind sharing the arxiv link to your work?