I have a problem that I'm not sure would fall under stuttering... but it is a speech imepediment, though it's only developed over the last two years. It's escalated to the point where one of my roomies thought I was having some sort of psychological attack (the exact term she used was "word salad", since I couldn't get out maybe more than two words). Generally, I don't do the "T-t-t-time." thing. Instead, I'll be talking and letters or sounds will either vanish, slur horribly or be completely impossible to understand.
If I said "I'm going to the store to buy some milk."
It might come out "Em gowwnk to saa store to byuuh smaa mikk."
It gets much worse when I'm stressed or worried. I used to have quite fluid speech and very little accent, so this is quite baffling and puzzling for me. It's extremely annoying because I can't talk right and I know it. I can hear exactly how I'm talking and no amount of effort will put it right.
Do you have a univesity near you that with a communications and linguistics department? Maybe contact them, and see if they know of ways to help you - like studies and things - that might not involve insurance or much money.