I had eye surgery carried out in Bumrungrad hospital Bangkok. I contacted them with my UK macula degeneration diagnosis. They confirmed this with my UK eye surgeon. A treatment plan was devised and a medical visa obtained. This was before DTV existed, but it should be the same procedure now. I had an IMT implanted into my left eye, with three months of recuperation and training, then surgery on my right eye was carried out. In all, this process took eight months. Bumrungrad hospital are very professional and can provide any documentation needed. They have helped lots of international patients.
Your best course of action is to have your sponsor bank the cash into your bank account, but even then, you might have to wait until it has been in your account for three to six months. It is ridiculous that each embassy can make up their own rules, but that's the system that we have to live with. Good luck.
Although not asked for, as I have a copy of criminal record search because I'm a British passport holder with an American journalist visa, I supplied it. No comment was made by IO.