Those midfield options are so poor.
Fabian Delph hasn't started a single league game since 26th December.
Ruben Loftus-Cheek hasn't started a single league game since 2nd January.
Ross Barkley has started just 4 of the 9 games since 2nd January.
Henderson and Rice are really the only ones who get consistent game time and I am not sure you can really play those together. 3 left backs and 3 right backs in the squad too.
Though looking at it, you've missed out Dier in midfield, but even then he's started 1 game since the 8th December and much like Henderson and Rice is a bit on the defensive side. Should probably start looking to develop himself as a right sided centre back in Southgates three.
I think it might be the case where Dele may need to be dropped deeper in midfield. Put him and Rice in there together with Rashford, Sterling and Kane up top.
Refuse to believe there is no talent in the Championship that could be called up
Agreed the midfield options aren't great in this squad, partly because I think Winks is the only top CM England have who is creative, but I think Loftus Cheek is ok, although as you say Chelsea aren't playing him.
Barkley hasn't yet got back to his pre-injury form and I suspect his lack of playing time isn't helping him.
Lewis Cook (Bournemouth) is injured but might otherwise be in the squad, but again is more of a DM.
Ward-Prowse (Southampton) is an option, and a decent free kick taker, and I suspect at some stage one of Delph, Barkley and Loftus Cheek might drop out to accommodate him - might also trigger one or more of the three to move to a club where they are playing more regularly which would help.
James Maddison was dropped for this squad, but I think will be better next season having had a full PL season behind him.
In terms of Championship, the obvious candidate is Grealish, but the problem (other than he's just back from injury) I think is that the championship is a step down from PL and with it he's not used to playing with the higher quality players, which means he really needs to move to PL to play. There are examples of course in years gone past where players have even been picked from the 3rd tier - Peter Taylor was playing in the old Division 2 when picked for England - so maybe Grealish should be picked to train with England to see whether he's good enough to play for England.
I can see why Dele dropping back solves the cm problem - but personally I think the Kane/Dele combo is so good that I'd try not to do it.