Many people are telling me that regardless of that $6,000, now's the time to buy. My plan is to systematically pay off that card while saving at the same time to have an emergency reserve should push come to shove and I'm in a financial bind. I want to go into the home buying process with only my student loan debt to worry about. Outside of paying off the card in its entirety before purchasing a home, what other options do I have? With the market the way it is and my good credit score (730-ish, debt-to-income ratio around 10%), I'm sure there are options available to help me obtain a home faster.

I would suggest you try to find a fixer-upper that is priced right. You can get in the home, fix it up and then get a tax deductible heloc to pay off the credit card in a defined time period. In your situation, I wouldn't go with an all out rehab, but try to find one that needs some cosmetic work. Paint, curb appeal, etc. You only need it to appraise for slightly over the purchase price to get the $6,000 out in a heloc.

PS. You are ALWAYS better off building equity in a home as soon as possible. Unless you are living with relatives for free, you are throwing away money on rent.