Got rid of my Sony RX100 – will E-PM2 with kit lens address its shortcomings?

That's not what I said. The kit lens on the E-PM2 is, I think, better if you stop it down than you get with compact cameras like the RX100. Just my opinion, but I think I'm good at pixel peeping. (At some focal lengths, it's not very good wide open.)

Yes, I think that if the OP spends $499 for an E-PM2 he will get what he's looking for, albeit with Image Stabilization that may not work, see this E-PM2 review.