I have been in the Home Building/Real Estate industries for over 16 years. I have actually personally worked for several of the Big Builder's here in San Antonio and consider myself an expert in the new home construction arena.
I know of several good Builder's that have move up programs and I, as your Realtor would certainly be willing to work with you on the listing of your current home in Round Rock, while representing you on the purchase of your new home.
All the best to you in your home search.
In the contract to buy a new home here, they would put in a caveat (a condition) that you will proceed to purchase a home based on the sale of your home in Round Rock. This usually applies on 'To Be Built" homes and not the ones already begun. Since there is no way to determine exactly when your home will sell, it would not be in the best financial interest for the Builder to hold a specific existing one for you.
I closed on a home last October for my clients from Seattle, who picked out their floor plan and lot and put a deposit down. They had the same stipulation that you are in need of. Construction for their home began once the Builder had a copy of the Executed contract and the "option' period had been passed.
Where there is a will... There is a way.