Also note that the stabilization in both the G7 and NX500 is lens based. i.e. you need to make sure the lens you use has stabilization built-in (not all Pany lenses do, I don't know about Samy).

I also don't think the NX500 has an external mic jack.

I point this out because I think you're going to have to compromise somewhere, and I think your two best compromises are:

Panasonic LX100 which has stabilization and a lens that's good for indoor/low light parties, but no mic jack.

Olympus E-M5 (original) which has come down far enough in price now that the Mark II is out (B&H has it for $500) that you can add a 25mm f1.8 lens and SEMA-1 mic adapter within your $1,000 budget. This will give you 5-axis IBIS (In Body Image Stabilization), good indoor/low light performance, and a mic input, but not 4k video.

Having said all of that, I still believe most people would be better off shooting video on a dedicated video camera.