Leaving another reference here: Levo Gen3 MY2022 > connected the old SRAM brake hose (Code RS brakes) with the Hayes hose using an M3 threaded bar going into the larger Hayes hose, and std threaded barb going into the SRAM hose. Adapters came with a Chinese brand hose assembly kit. At first, there was no way getting the interface fed into the chainstay from the rear, larger OD Hayes hose would always catch an edge of the frame or the guide tube inside the frame. I re-did the interface to make it as seemless as possible, no spaces or steps in between. Then I was able to pull-push the assembly from rear to front without major issues, though it was a sturdy pull. However, just after exiting the cable passthrough in the front, my interface barb snapped out of the Hayes hose. LUCKY ME, shoudn't have happened any earlier. Like this, I was able to pull on the Hayes hose end itself, pulling the rest in.
Side comment: I used some SRAM DOT butter on the outside of the Hayes hose (first 5 inches) to reduce friction. Not sure how much it helped, though.
I'd say, generally it IS possible to mount the Hayes brake hose into Levo 3 frames, but there are some catches..