My little Siberian probably shares some of your Maine Coon caracter. She is definitely very affectionate... but... with a pinch of self respect, which I haven't seen in any of my other cats (not siberians). She will make her demands of attention on her own terms... whenever and however she wants. She faithfully follows me around the house, just to make sure she doesn't miss something important, like the weekly litter cleaning... hence that she actually inspects it to see if I really did a good job.
Generally, I think Maines and Siberians share a bit of that dog-like caracter. They are loyal, joyful companions, yet, they have a certain independence and dignity. They are also a a tiny bit possesive, as many cats are, which might explain why they all fight for your attention.