Well rule one... refinancing is not free. You will have to pay something like the closing costs again. Over the life of your loan, this might not be a bad idea. I am pretty sure you can refinance with a bank, but I don't think FHA will make you a second loan.
Rule Two... The days of unsecured house loans are gone (maybe this has changed since I last checked?) To move your loan to a bank, you will need at least 20% equity in your house.
Rule three... Find a bank that agrees to hold onto your load for the term of the loan. Some banks will write your loan then immediately sell your loan to a quick foreclose artist, and you could be foreclosed on is as few as 3 months from your first late payment. If it is a local bank that mortgages other houses in your same neighborhood they have a vested interest in making sure you make good on your loan. As long as you pay something each month they will not foreclose in the event of a job change etc etc etc.
Once upon a time a adjustable rate loan was a good deal. For the time being, you want a fixed rate loan.
Make a house payment every four weeks, not once a month. Every extra dollar you spend paying down your loan now is like $7 5 years from now.
Finally, consider selling your house and renting instead. Home ownership is for chumps, and it is a huge material investment for little or no return. Instead of improving your house (which will not increase its value as much as you spend) look for an unsalable flipper, fix that up, and sell it, or better yet make it an income property. There are still stupid numbers of foreclosed vacant homes on the market.
my $0.02