My Dane experience is a mix - probably lab, maybe some pit... mostly all-american mutt (best guess).
He was a GOOF. Very happy-go-lucky, and willing to please - including being a good couch-slug (we are like you in that affiliation). Not much of a protector (he was pretty submissive), but he did alert us to the postman or UPS coming to the door. The lab part of his genes did come though pretty heavy, I think.
We have neighbors with Danes, and they also seem like big goof-balls. They do alert when people walk by, but are very nice and calm on the leash.
I would say, relative to an EM, very comparable - and depending on the specific dog in question - maybe a little more energy, a little more social, a little taller... but all in all, I think very similar and would conform to the household just like an EM.
We also have had some strange rescue interactions - first with our Dane/mix puppy, who was being shuttled around with his litter between multiple houses like checkers on a board. The foster mom let us come grab our pup before their last move - which none of his siblings survived... they all came down with severe parvo.
I would still try to find a good rescue group in your area, though. I think fostering would be very rewarding (and demanding, and time consuming, but, still... rewarding).
We have a group in our area:
Old Dog Haven, that specializes in senior dogs. I'm hoping to become a foster for them once our senior cat moves on to the rainbow bridge. I don't want to put her through the stress of strange dogs in the house at her age (17.5), but I think Denna would love to have another dog in the house.