Chances are, your current house payment is more than the next buyer's house payment will be. Have you seen the rates? If you can rent back your current house somewhere in between your payment and their payment (for a short time - a month or two) until you can close on your next house, you both benefit. Nothing would keep you from finding your next house now. You could narrow down your choices and define the area now, and just hold off contracting until you know you've passed all critical milestones on your existing home sale. We're doing it ALL THE TIME for folks right now. They save on moving expenses, and in many cases the buyers are happy to let you rent for a few months. It gives them time to save and pay cash for things like window coverings and landscaping - usually the first two costs once you move into a home. People are paying down-payments and paying for their closing costs these days. Any time to rebuild reserves is a blessing.
There are plenty of loan officers out there who will tell you that you can buy that home and still hold onto the townhouse. But, I can site case after case of Underwriters who tied up the process with lots of questions and concerns at the 11th hour. They don't like to blatantly deny the loans, so they just hold up the process until you get frustrated and go away. Their stall is to give you time to get your current home under contract, so they have less risk.
As a buyer with no encumbances, you have strengthened your buying position by freeing yourself of the townhome first. The most in-demand buyer is one without any contingency. In this economy, that comes with negotiating power.
I would not steer you wrong. I have no skin in the game.
Have a blessed day!