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.
It sounds like this is what you're describing...
If this is indeed what you've encountered, you should remove the grounding conductor from the twist-on wire connector used to connect the white wires.
The only place grounded (neutral) conductors and grounding conductors should be bonded (connected), is at the main service disconnect.
If there are no grounding conductors in the house, it's not that big of a concern. As long as the wiring is done properly, you should have no problems at all. If there truly are no grounding conductors in the house, connecting fixture grounding conductors will have no effect. If you're really concerned about the lack of grounding conductors, you can install combination ground-fault circuit interrupter (GFCI) breakers in the service panel.
This sentence also has me concerned...
I cannot use the metal ceiling box that was being used with the ceiling fan. I can only use the bracket, which is currently screwed into place, right into the "hole" in the ceiling.
Are you saying that the new light fixture is not installed in an electrical box?
If this is the case, you should correct that issue as well. All electrical connections must be made inside an approved, listed and labeled enclosure.
Best Answer
The deciding factor is whether the device is listed (survives UL etc. testing) for that use. The conventions for listings are as follows.
If it says "12 AWG", it is listed for both solid and stranded wire.
If it says "12 AWG SOLID" that means it is not listed for stranded wire.
So, if you have found where it specifies such things, and it is not specific as to solid/stranded, that means both.