First question for you; Wood or Plastic?,as Fitz made both.
What your probably going to have to do,is to remove some material from inside the grips,so the grip frames will fit "deeper" into them,thus sealing up the "gap" in the backstrap.
Have a pair of an Officers also,and thats what I had to do(plus reduce that thumb rest in size a helluva lot!-for my particular "hold".
Fitz tend to fit "OK",as far as length,but the Franzites,at least for Colt E frames(like yours) and the New Service,tend to be short,or "shrunk". So its either a gap at top of grip,or they ride up on the bottom,showing 'bout 1/8" of metal. Some of the more knowledgeble (or honest!) sellers on eBay will mention that.
Go slowly on your fitting,keep checking,and it will be easier if it is wood! Bud