If you’re valuable enough, and they like you enough to want you on their team, then I’d use that as a negotiating point before accepting the position. Tell them that you really want the job and you’re excited about it, but the only thing holding you back is $3,500 in moving costs. Exactly. And if the company is worried that you might move, take the money, and then quit in three months, let them agree (in writing) to pay it once you've been on the job six months. I realize this means you have to carry it in the meantime, but it might address their concern if they have one.
Just don’t forget that the IRS is going to get their share of that moving money.