I originally made this a comment, then realized that no one would see it. I'm not sure if this will actually be helpful to anyone but in the interest of closure here's what happened:

I used the smaller bottle cap, taping it tightly to the bottle with parcel tape and also using two rubber bands to keep it in place. The result was O.K. but not nearly as good as the first time I made it - don't know whether it was the cap or whether I did something wrong. The first time, after three days the result was an unappealing yellow color but very strong and certainly alcoholic - I could feel the effects after a couple of glasses. This attempt, after 3 1/2 days, was a nicer color that tasted weakly of ginger and was definitely not alcoholic.

I'll try making it again in the next few days and see how it goes.

Thanks for the suggestions!