I picked up a pair from a LE supply for $979 a pop. The 6720 is the zennith of KISS carbines.
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Heres what I did. She loves it. 14.5 inch Ballistic advantage light weight profile with permed Rainier RAC.
Aero precision upper/lower and UTG PRO slim tube. (The UTG Pro may be cheap but it locks up tight to the receiver and is straight as an arrow)
SLR Adjustable gas block, AIM Bolt.
Im guessing weight w/out optics is about 7 pounds. Could have been lighter (like mine below sans optics of course)but she had to have pink.
http://img.photobucket.com/albums/10...psa3zugzrv.jpg
OP, looks like you are on the right track.
Colt, and bcm would definitely be the two to look at for a general purpose, lightweight carbine.
I would suggest a lightweight profile barrel, 14.5" barrel with some flash hider perm. attached (or just a 16" barrel), midlength gas system, and the eotech she wants. If there are still funds available, maybe get a lightweight rail, but not a must-have. I like BCM since you can pretty much get exactly what you want, already put together, and you know everything is done right-straight from them.
bcm 14.5" LW w/12"dd lite or MI keymod $645-$685 respectively.
G&R bcm blem lower $372
G&R BCM bcg - $170
Gunfighter-45
TOTAL=$1280 with no sights
or go to G&R and get the bcm lightweight midlength rifle, outfit it with magpul furniture and buis and call it a day for $1186. Then get the RDS. I would definitely get midlength for the ladies. Both my, and my friend's girl thought the recoil difference between 16" carbine and 14.5" mid was significant.