I wouldn't do it.
1) A company that doesn't offer any relocation assistance is ridiculous- get with the times, it's fucking 2015.
2) Up heaving your life for an entry level role is not a good idea- it doesn't show progression and will limit you in the future.
3) You still haven't identified what we talked about in our 1 on 1 meeting that day, what is it that you truly want to do? I still think some of the struggles you have are because you have not identified the one area you want to focus- employers can detect someone that's all over the board.
4) To someone else's point above, if that role doesn't work out, are you really going to want to move back to Columbus just to keep job searching? I say you continue to search here and work your job that's guaranteed. You may not be happy, but you'll be even less happy if you hate your new job and you just flipped your life to get it.
Find out what you want to focus on and I'll help you find something from there, but until you narrow down where you want to spend the rest of your career, you'll continue to search until you do.