Back in the 70s, 80s and 90s, I had my own tailoring/dressmaking shop and I was frequently asked to do the impossible - things that no one else was willing to do or that someone else had attempted and screwed up - and in all those years, there was only one job I had to turn away because it truly WAS impossible. Had you come to me back then with this request, this would have been the second.
The ONLY way I can even think to do this would be to do some intricate cutting of the material you would need to add to accomodate the cover and drawstring for your hole and then apply something like caulking or duct tape over all the stitching to seal up the holes made by your needle - but if you don't care what it LOOKS like, I suppose that would be a solution. Unfortunately, there's no way I can give you a pattern here... I don't know where you live but you might take it to a sailmaker? Or an alterations shop to have the work done and then, when you bring it home, do the additional work of caulking/duct taping the stitches...
Good luck... I like weird stuff like this!