Honestly, I'd like it if there were no special battlegrounds that were rated.

Instead go with, you cannot enter with a group larger than five players (ie, no raid queuing), and if you queue for a random it is rated.
Have an individual rating (queuing as a group uses the average rating), and place you with others as close to that rating as possible, then be opposed by a group at near the same rating too.

You'd have the largest group of players in the rated pool; no issues with needing 2 more players for your rated raid.
BG's would play as they already/always did.
And it would be an alternative to arena, for those who prefer the world pvp/battleground style.