When a person transfers and the new home is more than 35 miles closer than the old home, he can get a new loan. Whether you can qualify to carry it as a second home or must sell depends on how much income you make. Whether you qualify at all then depends on whether the new position is with the same company and/or the same profession at a new company.
Generally, a first time buyer qualifies for assistance, but there are other circumstances that would qualify a person to get assistance besides its being the first home. An interview is in order to establish if one of the other possible criteria can be met.
Lowering your rate would be about lowering the rate on your current loan? If so, no lenders will re-finance a loan for someone who is unemployed and they dislike re-financing when you are about to convert the property to a non-primary residence or a rental. However, if you mean could the new loan on the new house be financed at a lower rate than 6%, quite possibly. The bankruptcy plays a role in this determination. For example, if you have been discharged from bankruptcy by long enough. Your credit score is still important and will likely still be negatively affected by the bankruptcy.
Selling and buying appears, on the surface, to be the most reasonable scenario.
What you really need to do is discuss the matter with a loan officer to help you understand the alternatives before you bring a Realtor in to sell your current home.
We may want to work on a short term lease till you have employment, we work with clients for rentals.