I understand this is a confusing situation. In my suggestion, excellent credit will certainly help you. However, you being upside down, you may consider offering something more to your lender.
The first thing that I would strongly suggest would be to re-negotiate with your current lender. This is likely to yield maximum result.
Also, take note of the following. Generally speaking, lenders will require you to have a certain amount of equity (ownership) in your home, before they'll approve you for a refinancing loan. But when you are upside down, you actually have negative equity - you owe more than the property is worth. This is why so many people are being turned away when trying to refinance. They lack the equity needed to get approved.
In your case, irrespective your your lender, i.e. when you try with your current lender or at a new lender, offer to increase your equity, at least to the half of the amount of the upside down gap. This will increase your equity in your home and will place the existing or new lenders at higher comfort levels. This means, offer to pay more down payment, while applying for refinance.
Further, if you still do not succeed, you may contact HopeNow, which is an alliance between counselors, mortgage companies, investors, and other mortgage market participants. They will not only direct / guide you but will also liaise with your lender if required. You may reach out to them at http://www.hopenow.com/
I am sure this would help...
No Issues.. I shall opt out and let some other expert help you with...
Wish you good luck.