Good work, MsMS, you are playing both the financial and FICO game.
I have only one question... when are you planning to need your FICO score for the refinancing? If not within the next six months, then maybe using your new BoA credit limit and doing a BT with them to pay off the Discover might be wise. Since you are still at 61% on BoA, doing a BT from them to Discover will drive %util on that card back up.
I have my prejudices, for I am not a big fan of BTs unless it is for longer term (6 month or more) financial planning reasons, and not for immediate FICO reasons. A BT does not improve your overall %util, and usually costs you an instant 3% BT fee (not an annual fee), which, if you take it to the extreme, to make my point, would be a 36% interest charge if you did one every month for a year. One card goes down in %util, the other goes up, with no change in overall %util, and 3% out of pocket, gone forever. It is the longer term, low interest that is offered by the BT that is financially sound, so a longer term tool, and not of immediate benefit FICO or financial benefit.
Those CCCs dont offer all these instant checks and great BT offers because they are trying to benefit the consumers, and not themselves.Some can benefit with smart planning, but on the whole, most lose.