I see two issues.
First, if you see the house you want currently advertised and it is priced correctly...it will likely be sold in a few days. Not much time to get the equity out, specially with banks being so cautious.
Second, If you were to purchase the home "you really want"...will you be able to keep up to mortgages until your current place sells?
Give me the address to the one you really want and i will check to see if it is still available, lets take it from there and see if this might be possible for you.