It sounds like the group I DM for is rather similar to yours. It didn't bother me for years. But eventually, I wanted to run something that felt less like jumbled up Greyhawk!
Best success I've had so far is with tying PC background to the setting:
Sat down and gave a brief explanation of the setting before starting. (Kalamar in this case) Offered the players extra character building points for getting their background merged with the setting. Talked through the parts each player found interesting in more detail.
Ended up with a bunch of really interesting setting specific hooks, al of which were the players own creations. I just tied them into my metaplot. It cut down on the prep work I needed to do, served to introduce some interesting bits of the setting to the PCs and got them involved right from the start.
Found the 'carrot' of extra building points worked really well with my group. Also made me feel less guilty if there were bits of peoples backgrounds I never touched on.
I coupled this with using a small area of the setting - PCs ruled a small town (Eb'Kakido, IIRC). The rest of the setting would intrude from time to time, but they got to know their local area very well.
Wasn't perfect, but much better than my previous attempts!
Some other thoughts:
Having the PCs all belong to the same organisation can help. Especially if the organisations goals interact heavily with the setting. Makes things feel very different from the 'typical' adventuring party. Ex: Played in a Star Wars campaign - we were all Jedi Padawans - worked very well.
In the way of familiar worlds: IMO Warhammer adapts very well to DnD and a lot of players are likely to be familiar with it. The mix of magic, chaos and gunpowder works really well for me.