So you tried to add the CMYK. profile to your printer driver and it did not give you an error right?
If you have a CMYK device it’s no wonder that you will have better color using CMYK - LAB - CMYK than if you use RGB - LAB - RGB/CMYK
I mean every printer prints with cmyk ink right. So the chipset of any printer converts data to CMYK for printing. The “can of woms” is hidden in the driver because if it can accept only RGB data and you send it CMYK then you get double conversion that leads to wrong colors, or just an error message.