Exactly refinance. Then he doesn't want his name on the deed or mortgage. Great. But when I need to fill out the paperwork I will not be able to qualify for a new mortgage. At least that's what the banks tell me.
I am not trying to sound mean, but have you run the numbers on this? You can't afford this house.
Home value (you) - $410,000
Down payment - $10,000 (Assume you go with deal #2)
Total loan - $400,000
Interest Rate: 3.50% (I'm being very liberal)
Monthly payment - $2,346.18 (including escrow, 30 yr fixed)
Your income - $44,000 (gross) / $35200 (net, rough) / $1,353.85 bi-weekly
That's like 86% of your take home pay. Of course your bank will not refinance your loan, you simply cannot afford it. I hate to tell you, you would be best served to sell the home and find something more affordable.
As for the division of property, it really depends on how your state views the comingling of funds. One thing I will tell you is that if the two of you can reach an agreement without going to court, it will save you a lot of money. You have already figured out that lawyers are just out for money, do without them as much as possible.