220V 3-wire ground install

My home was built using the steel boxes and EMT for the ground circuit (no ground wires anywhere). My oven is currently wired with 3 conductors (2 hots & a neutral) run in 1" conduit. I want to replace this wiring with NM wire so that I can finish the basement ceiling without the conduit obstructing.

I understand that I will need to run 6/3 with a separate ground. My panel has no separate ground bar so I'm wondering how best to proceed? Seeing that the neutral and ground are bonded in the panel is it ok to connect the equipment ground from the oven to the neutral bar?

Your logic is correct, but are you even allowed to run NM cable? Chicago is EMTland, but I know this extends out from there.
If you are in Wisconsin I would definitely check to see what the local codes are.

Thanks for the reply Petey. I can't find anything in writing saying otherwise but I e-mailed the local building inspector to see what he has to say about it. I'll give him a couple days to respond before I try calling him.

Chicago is EMTland, not Chicagoland. My house is about an hour north of Chicago and 30 minute south of Wisconsin. Here and a lot of other cities are all NM besides multi-family and commercial. Some require AC, but its better than running conduit everywhere. They still don't like plastic boxes and really don't like PEX, but NM is just fine.

Sorry for the delay in closing this one.
I talked to the inspector- we can run NM as long as it is protected (between the joists). We have to pull a permit and get it inspected which is fine.

Naturally the permit costs almost as much as the materials required.