Well, I am not that far along in my transition, I certainly havent paid for srs yet, but I do know a thing or two about saving.
As you mentioned saving up money and having the cash on hand to cover it is the most straight forward method. Look at it like this revenue - expenses = potential savings rate (r-e=p for simplicity's sake). So if you cannot reduce e then perhaps it is possible to raise r, basically i found at my last job no matter what i did within reason there was no way to reduce my exspenses enough to really save, so increasing my income was the only way.
Of course, there are ways aside from traditional jobs to raise money, there have been a few people who ran blogs that had srs donations, and while i cannot say how successful such a thing would be. A friend told me I should raise money with a bake sale, despite how cliche that sounds gathering some friends and doing something to raise money isn't such a bad idea.
Our society is also driven by credit, I have heard of a few people paying for ffs with thier credit card, now you say you are mostly at your credit limits but, getting enough extra credit to afford it is likely easier than getting enough cash to afford it.
There are also illegal or unethical things, the most common I can think of are private student loans that are taken out and spent on srs rather than school. I dont think people should co.wider doing anything more unethical than this, I doubt for example very many bank robbers get away these days.
There is also health Insurance, some policies do indeed cover it, though I am not versed on the particulars I am sure others here are more helpful with that.