Not sure where you are getting your information from, but FHA loans ALWAYS have PMI. Upfront PMI of 1.75% of the base loan amount (which can be financed into the new loan) and monthly PMI. The only time you can get the monthly PMI waived is when the LTV goes to 78% of the original loan amounth.
As far as appraisal re-consideration goes, it is very, very difficult to get done today. Realtors telling you what they would list your house for is meaningless and the county tax assesor is not an accurate determination of value either. The only thing that matters really is closed sales of comparable homes in the last 12 months.
Based on the appraised value of 197,500, it sounds like you are looking at a new loan amount of 190,587 plus 3,335 for the up front mortgage insurance for a total loan amount of 193,922. If you have 190k to pay of on your current mortgage you will probably be looking at bringing around 5,000 cash to closing, because your closing costs will probably be somewhere between 5 and 6 thousand. It would definately be worth it though to drop your interest rate from 6.5 to 4.875.
Good luck.