Is an upgrade from Lumix G3 viable for a noob photograhper?

If you believe DXO, the only improvement from the G3 to the G5 and G3 is ~ 1ev in dynamic range.  They claim color rendition and noise to be essentially the same.  GX7, GM1, and GM5 all give you an extra bits worth of color (from 21 to 22), another 0.5 ev, and supposedly similar noise but the consensus I've seen in reviews is that they're good for another stop, that 3200 vs 1600 the OP mentioned.

So unless you're really hankering for a larger grip or some of the newer features I don't see the G5 (especially) or G6 being much of an upgrade.  The GX7 would be better, though you say you like the DSLR format, and you have to think about whether you'd miss the articulating screen.

One thing you don't mention is if you shoot raw or JPG.  I also use a G3 and have found that shooting raw and making pretty minor adjustments to the processing has had a big impact on the quality of my pictures (I picked up Optics Pro 8 when they were giving it away for free a few months ago).  I mainly take pictures of people and find that the G3s pictures almost always benefit from a little increase in the white balance color temp (50-150 K), small changes in tint, a +5-10 in vibrancy, and sometimes judicious use of the selective tone adjustments.

So my vote is either to get a good raw developer and learn how to use it, or get a new lens that will allow you to take different pictures than you can with what you have.

As said I use a G3 and see enough pictures taken by people more talented than me with similar or lesser cameras to know that my own skills are more of a limitation than the G3.

jeff