I am assuming that the stenosis is in the canal of the valve or is it at the opening of the stoma?
I have had my valve "sink'" which caused the opening to want to close up because nothing was keeping it open...and a crooked valve...neither could be fixed with a catheter...but, you may get help from keeping the tube in or a plug...you need to keep them in at least 30 days for it to scar in. Yes, it can work, yes, it can help, you just need to be patient and give it a chance to do its job...meaning allow it to build sufficient scaring to hold things open and strait.
Do what the doctors tell you to, do not eat chunky food, stick to blended veggies, soups, proteins and nothing that requires you to pull the tube out to clear it.
And then, give it an extra week over and beyond the month. For security sake...
I hope that it works.