Whatever you end up doing, I recommend against connecting #10 solid wire directly to the lugs of the EMS and only use stranded. This is a photo of our EMS before I changed to stranded. You can see that the solid wire only contacts flat (or near flat) surfaces of the lugs on two opposite sides of the round copper #10 wire and IMO does not provide enough surface contact area between the wire and lug. I have read of a number of instances of an EMS overheating and in some cases, a fire and I suspect that the design of the lug could be a factor when terminating solid wire.
The better way to terminate the incoming #10 wire (shore power) is to use stranded and if needed, you can splice a short lengths of stranded to solid inside the EMS. For splicing stranded to copper, I recommend using vibration resistant wire connectors as they make a more reliable connection.
You could run stranded #10 from the EMS to detachable cord outlet using a length of your old cord.
FWIW, I also converted to a detachable shore power cord (on a previous TT) and ended with an empty box where the cord used to get shoved into. Turned it into much needed extra storage space which was a nice bonus to the project.