tl;dr:
- I though about SL1, but can't see it being a solution because lenses are large, other than pancake, and pancake is too long on AP-C.
- Nex is the best overall compromise with powerzoom 16-50: budget version is Nex 3N, splurge on yourself is Nex 6
- Fuji X10 is weirdly attractive and fairly versatile camera, if you buy used for not too much money
- Nikon V1 is good beach camera for parents of small kids, if you can still find it on clearance
Long explanation:
I had same dilemma (find small body to accompany my 6D) and I tried, bought, stole, sold or borrowed many, many camera trying to solve it: Canon G15, Sony RX100, Panasonic LX7, Panasonic GF5, Oly PM1, Nikon J1, Nex F3 and 5R, Sony A57. These are all gone, but here are ones that are left:
Sony NEX 3N with powerzoom - great compact solution for $500. If I were not stingy, I could have gotten NEX 6 with the same lens for few hundreds more - grip itself may be worth it (plus EVF, and faster AF), but IQ is the same.
Fuji X10 - very beautiful object, and tactile experience camera. I keep thinking I don't need sensor that small, and I keep being surprised with quality of the pictures and colors. I bought it twice: I returned new one I bought (too expensive), but then I bought used one as it kept bugging me, and has some magic draw for me. It could be leather case

, or maybe I'm ok with throwing $300 on a gorgeous toy? The only compact camera to not disappoint, and yes, I prefer it to RX100, though technically it's not better... Not sure about X20, supposed to be better, but sensor is a bit more traditional (though NOT traditional), and X10 sensor has couple of neat tricks that I love....
Nikon V1 - I just picked up one on ridiculous sale for $299. Not impressed with IQ, but AF is insane, and because of small sensor, even when it misses, deep DOF usually saves it. Good ONLY in good light (otherwise average)!!! But great parents camera for outdoors, silly good 60 frames/sec and great slow motion mode. I'm still debating if I should return it (I'm still inside of 2 weeks return period), but I'm taking my twins to Greece soon, first hot vacation, and I enjoy though of footage and pics that may come out of it, just because of the speed of the camera. Otherwise, inferior to both Nex 3N and Fuji X10 in terms of pictures appeal.