Force Carbonating Root Beer in Bottles

I am thinking of ordering Sprecher Root Beer Syrup. My plan is to mix the syrup in a bucket and fill two liter bottles, cool them down, and use a carbonater cap to apply 35-40 PSI while shaking the bottle until It looks carbonated. Could I then just let the bottles sit for a few hours to settle and pour from that point? This way I wouldn't ruin a beer keg. Is this a bad idea?

I dont think is such a bad idea if you want a quick fix for the kids but the unfortunate thing your missing out on is the important flavor of the yeast, similar to beer traditional root beer got much of is flavor from ale yeast these days for a modern taste you can use wine yeast ec-1118 . How ever inconvenient it would be to use up a keg it's still a good way to go you can cask condition to ensure your yeasties leave their flavor but not have to worrie about sediment getting in to your finished drink!

Honkey,
Sprecher syrup has preservatives in it so it can't be naturally carbed by yeast.

Happybrewer,
That sounds like the way to go.

Yep, that'll work fine. Make up the mix, and then chill it. If you put it in 2L bottles and use the carbonator cap, you can set the psi at 40 psi and shake it. I then disconnect the co2, shake some more, and give it another blast. Then shake some more. Within about 5 minutes, it's carbed up pretty well! You'll need a different carbonator cap for each bottle, unless you only made up 2L at a time. Since my kids are now grown up I only make 2L at a time. I forget the exact measurements, but it's 4:1 I believe so you'd use 1 cup of syrup to 4 cups of water.

I like doing it this way- first, no yeasty sediment in my soda and secondly, no root beer flavored beer line! I do have an old keg that I used for rootbeer years ago, and I never did get the flavor out of it.