The thing to remember is that the propane coming out of the extend-a-stay is unregulated......it comes out at full pressure so if your BBQ has the regulator built-in it will be fine. You mentioned that you use 1lb bottles so you should be fine.
If you are trying to use a BBQ that has the regulator at the tank attachment and you plumb the hose directly it will have too much pressure.....if you have this kind you will need to make a connection after the regulator.