Can we go from an ARM to a fixed with a loan modification agreement rather than doing a refinance?

That is a question for your legal counsel, but it does not seem to normally be out of the question..

Is this question regulatory in nature, or contractual? Whether to, and how to recast of a contract in a particular way is a matter of state law--to be discussed with the bank's attorney. If you're only concerned about the regulatory coverage, then look at Section 1026.20(a), OI #3. It explains what is and isn't a "refinancing" (for Reg. Z purposes, only) when variable rates are involved.