We recently bought a new home. I had 20% down payment but at the last moment went with FHA loan since I was afraid with the Florida housing market. THis is our primary home. The lender assumed I did my homework and didn't question my move from 15 yr conventional to FHA loan. He thought I did my homework and just mentioned about the 1% FHA fee that is bundled into the loan. We thought this is fine since we are doing only 3.5% down payment.
My lender knew my credit score is 732 but still didn't question my move from conventional to FHA at the last moment.

So we did the closing and I started working out plan for next 2 years. I always assumed that I'll wait for the market to steady in next 6-12 months and payoff to reach 78% LTV so that the FHA MIP goes away. Now, the following came as a big surprise to me

1) The FHA MIP doesn't go away for 5 years
2) The FHA MIP amount stays the same even though the principal goes down every year

I am really upset about my move to FHA and I want to get out of it asap.

Loan is $283K and 3.75% fixed interest FHA
P+I = $1274
MIP = $259

I asked my lender that he should have atleast advised me to do 5% conventional with PMI. That PMI would have been $165 plus I would anytime give away remaining principal to reach 78% LTV and get rid of PMI. Also, my lender told me that I shouldn't be that upset because conventional interest rates are more than FHA.

I really need some guidance here as I am a first time home buyer and went wrong with my first big financial move.

Should I refinance to 15-year conventional right away or refinance to 15 year FHA which gives me the option to pay off and get rid of MIP?

Please advice!! Thanks