Suggest a Funding / Timing Strategy for my Situation

[P M]

Greetings- here's my situation.

I live in a townhouse with a tremendous location in a college town. I am about to refinance it from 6.875% down to 4.875% and cut my monthly payment by over $200.

Then I would like to buy another house down the street, move into it as our primary residence, and rent out the townhouse.

Here's our dilemma: we need to figure out how to get through the transaction. On the other side of the purchase of the second house, we save enough income each month to cover the two mortgages even if we don't rent the townhouse.

Some details:

Townhouse- when refi'ed, will be $120k loan, 30-yr fixed, at 4.875%, monthly payment P+I = $635.05
Townhouse monthly taxes = $155
Townhouse monthly insurance = $21
HOA Dues = $120
Prop Mgmt Fee = $85

Monthly rent = $850

Desired New Home

Likely purchase price = $260,000
Mortgage rate 5.1% (???) for 30-yr fixed
P+I = $1,222
Taxes = $374/month
No HOA

I have $16,000 in liquid assets right now. I will likely liquidate $2700 on the townhouse refi, bringing me down to $13,300. I don't want to be completely devoid of cash- maybe I'd use $10,000 of this money?

I could also theoretically get a HELOC from my credit union up to 90% LTV of the townhouse. This would get me about another $10-12,000. However, the second house will probably require close to $30k in closing costs and down payment even if I get a 90% LTV on the house.

How would you find an extra $10-15k to get through the transaction period?