Hi Element116,
I've got the same setup as you (although I'm only averaging about 15-16mph, probably because of all the darn stoplights on my route) and I was contemplating the same thing.

I'm curious, assuming you buy a new 36V 10.5 Ah battery and hook it up in series with your older battery, will there be any problems with using 2 batteries which are not exactly the same ie presumably the older battery will have slightly less capacity.