Yes you are probably right, sorry - off my head only 1.1. can be powered from the battery port.
Actually, I am convinced that it is way more convenient to have a battery pack attached to the cable, and inside your pocket, rather than attaching it to the top of controller, making it heavier
IMHO possibly the most cost-effective solution is 6 AA or 6 AAA batteries - especially if you already have them: get a cheap battery holder:
http://www.pololu.com/catalog/product/1156
put your cells in and you get a lot of time on batteries. AA cells NiMH have at least 2000 mAh, AAA around 900/1000 which will provide you with plenty of playing time.
If want you use a 9V rechargeable, I'd suggest getting a 9.6V like this
rechargeable.http://www.atbatt.com/product/24293.asp
that also has a good capacity (230 mAh)
More pricey (as you need a custom charger) but probably good for 9V
http://www.batterymart.com/p-r-li9600-9vol...on-battery.html
http://www.batteryjunction.com/ipowerus-9v-500.html
Probably 6xAAA or 6xAA is the cheapest solution. In terms of capacity 6XAAA is twice as much as a LiPo 9V, 6xAA 4 or 5 times more.