I've actually slightly looked into this. This will be quite brief as I don't have time but I do appreciate that it could be seen a problem; but it's a good problem to have. We don't have a proper dedicated number 10 in this team and I'd like that option. I would say play James out wide as a wide playmaker (David Silva style) if you want to fit him in with Costa and Batshuayi. It could work.
If Conte is truly serious about the 4-4-2 then we can fit them all in, we have a few solutions. Currently, if we we're a side confident in possession we could field something like:
Hazard - Costa - Batshuayi - James
Fabregas - Kante
Azpi - x - Zouma - y
Courtois
*Azpi plays left back to help cover Fabregas' defensive deficiencies. We bring in a smart defender comfortable at playing the high line at x, and bring in a smart fullback at y who can support Zouma and Kante on the right hand side, whilst providing an outlet out wide on the right with James.
Of course, this is an extremely offensive team, and if we had need for more defensive cover we swap out Fabregas for Matic or Chalobah - or drop Michy or Costa and go for a 4-5-1 look:
Costa
Hazard - Fabregas - James - Willian
Kante
y - x - Zouma - Azpi
Courtois
*Again, if we need more defensive cover in this formation - drop Fabregas - I think this is okay though as he's being flanked by Kante, Azpi and Willian.
My ideal choice for y? Young defender at Milan called De Sciglio who is adept at playing both sides of the pitch quite well. Conte will know him well and it gives us great flexibility.
Basically, this only works because of Kante's superb ability as a midfielder to cover gaps. Kante signing is huge. As Ranieri said, the guy is pretty much a 2 in 1 player. That's how I'd approach the problem anyway.