I am a homebrewer, and even though I am no expert I feel I know a good amount as of now. It is normal to get your root beer to fizz over in small bottles. I also use champaign yeast. There is no better yeast for root beer as far as I am concerned. Im also not a big fan of molassas in any root beer recipe. I use brown sugar to take place of white sugar and molassas.
Throwing the root beer in the fridge will make the yeast go dormant. Maybe not 100% but at the very least it will slow down their activity quite dramatically. I recently had success in carbonating 12 16oz bail top bottles. Lets just say that I measured the yeast using the tip of a sharp knife to scoop it out of the pouch. If I could put a numerical quantity on it, id say maybe 1/16tsp.
I dont know if it would help but I do have some videos on YouTube that may help in your "getting started". Just go to YouTube and search my name "KD0RVY". Thats a zero not an O. Its my ham call sign.
Hope that helps you some.