Here's your solution (since I'm in the mortgage business I think about these things in my sleep) (1) Take a cash out refi on your primary residence to finish the home you want to be live in. (2) Get the right mortgage to do it. NOT soliticing here, but I've got access to a mortgage that will give you a $600.00 per month payment on a $200,000.00 mortgage. This type of mortgage will provide the cash you need to finish your home and in the meantime won't strap with some huge payments. (3) Or...get a construction loan with "Interest reserves" built into it. Interest reserves allow you to take up a year to build without making a single payment. In effect the loan is constructed with the payments for the first year built right into the loan. See.....done, case closed. You don't have to find something else to live in and you get what you wanted. You can PM me if you need more help.
As a final thought, I do agree with XU on the topic of retaining the current property, it will always make you money. If you can rent it out now, it will be worth far more in ten years from now and at that time you may want to sell it and take the profits. Two things occur there, (1) You will get the benefits of the interest right-off (tax deduction advantage) (2) Your renter will be paying the tab for the next ten years.
Take todays value and calculate a compounding return at 8% average increase in value. Since I don't know what your house is worth today, it's impossible to do the calculation. At any rate, once you have that, you can get an estimation of "future value" relative to present value. This should help formulate and shape your decision making process.