You should be able to refinance the mortgage into your name at this point. When refinancing a mortgage that is currently in someone else's name into your name, there needs to be a continuity of obligation. Since there is so much equity I'd recommend you look into conventional rather than FHA. The rates won't be great because of your lower scores (unless you are OK with a 15-year fixed, something you should look into), but you won't have PMI so it should balance out.
Continuity of obligation exists when:
• At least one borrower is obligated on the new loan who was also a borrower obligated on the existing loan being refinanced.
• The borrower has been on title and residing in the property for at least 12 months and has either paid the mortgage for the last 12 months or can demonstrate a relationship (relative, domestic partner, etc.) with the current obligor.
• The loan being refinanced and the title to the property are in the name of a natural person or a limited liability company (LLC) as long as the borrower was a member of the LLC prior to transfer. Transfer of ownership from a corporation to an individual does not meet the continuity of obligation requirement.
• The borrower has recently inherited, or was legally awarded, the property (divorce, separation, or dissolution of a domestic partnership).
You would meet the 2nd bullet point above. You can do the refinance as just refinancing what is owed or taking cash out (for the home improvements).
If you take a 15-year fixed (which improves chances of someone with lower scores to qualify for conventional) I bet you'd be fine to qualify, even a 30-year fixed could work out... but really compare the payments, because at your income level you could probably afford a 15-year fixed.
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