The first try at homebrew soda didn't work out. Altivo suggested trying champagne yeast rather than baker's yeast. Looking around, I found a source in the Twin Cities and asked sistaur to see if she could obtain some Lalvin EC-1118 (another site says it's, "Also great for carbonating sodas.") since she was going to be sending a parcel anyway.
That parcel arrived today, with the new yeast. I've started another bottle and am now in the waiting stage, again. The baker's yeast will get used for bread.
I did go to the store to get some more vanilla. As this is still just experimental, I went with the cheapest artificial vanilla. Curiously, it was the only vanilla that didn't have corn syrup in the ingredients list.