How about an EMT slip on bushing?

This about explains it all.

Catalog Page

EDIT: I think there are three goals here - clamp the NM cable in place, protect the cable from the sharp edge of the EMT, and secure the EMT to the jbox on one end.

I showed you how to protect the romex coming out of the EMT.

To secure the NM cable in place, where you want to clamp the NM in place depends on the box. If its a plastic box the most of them have their own clamping system. If it's a metal box then use standard 2 screw connectors, like these:

Staple romex as specified by code:

As for connecting the EMT to box, you probably need a metal box for the knock out. Use set screw connectors, you sound as if it is inside.

The EMT should be secured to the walls. You clamps will look like these. If it needs to stand off the wall use the first, which you might need if you don't have an offset,

Pipe Calmp

1 Hole Strap

J-Nail

Many other ways to do all these things also.

The only other thing I can think of is, an EMT connector, a rigid threaded coupling and two screw romex connector. Romex stapling by code.

You've got a couple of options.

THWN Conductors

You could simply run THWN conductors inside the lamp post.

Underground Feeder (Type UF) Cable

You could also run a smaller gauge UF cable inside the lamp post.

In either case, you'll want the conduit to come up above ground. Either inside the lamp post, or next to it, depending on the post.

If the splices are underground, you'll want to use a splice method approved for wet locations. Conduit underground is considered a wet location. Even though the splices may be in a conduit body, it's still considered a wet location.

If the lamp posts have access panels built in to them, you can make your splices inside the lamp post. This would eliminate the need for a handhole or conduit body.