You can mix them. All of the birds in my signature, like Froggie, live together and do very nicely. You can even mix bantams (if you're ever interested) and large fowl birds, even though there will be a size difference. Bare in mind that you said large eggs were a want, and Silkies aren't great eggers.
Trust me, I know.
In my experience, my bantam Brahma is amazing. She goes broody, forever wanting to be a mommy, but she is really the sweetest thing and when she's not brooding, does give a good amount of eggs. She is very friendly and personable. But also very submissive.
We also have a large fowl Columbian Wyandotte. She is also very friendly and personable, as well as submissive.
I had 2 Silkies but the rooster was a constant attacker and went after me and my family. He was a brute, a beast. The hen however is a love. She is smaller than normal, possibly having to do with bad genes and the way she was born? We really don't know. She lays soft-shelled eggs (eggs without the shell) and no matter what we do, they never come out right. We let her stay in a semi-broody state as not to lay these shell-less eggs (the other chickens will eat them if given the chance) and she does fine. Chickens won't lay eggs when they are broody.
And I don't have Welsummers but they lay very dark brown eggs.