There seem to be a few issues: 1) the Kings starting games slowly; 2) lack of interior D, and 3) the SF position.
As best as I can tell, the Kings have a tendency to start games slowly primarily because of two players - WCS and Fox. I would not want to take Fox out of the starting lineup because he is the most talented player on the Kings, age 20, and you need to let him figure it out. On the other hand, WCS is 25 years old and in his fourth year and should have figured it out by now. He has a tendency to not play hard and tough until his back is up against the wall. Bagley, Giles and Koufos don't seem to have a problem with starting the game strong. I would start Bagley and play him about the same number of minutes; he's played 33, 30 and 27 minutes respectively in the last three games (and was injured in 2nd half of last game). It seems to me that Bagley, though rough around the edges, gives you everything WCS has plus more. He would compliment Bjelica nicely and Shump and Fox and Hield, who I think should start. I wouldn't just play Bagley at center, however. During the course of the game, I might switch him over to the pf position.
Because I think WCS plays better with his back up against the wall, coming off the bench might be exactly what he needs. If Joerger tells him he's making the lineup change because he needs consistent effort on the defensive end of the floor and that he think Bagley gives him more of that than WCS, then Willie might get the message and actually try to block some shots and play D on a more consistent basis with his fewer minutes.
A search party should be organized to find Koufos and give the guy some decent minutes at the expense of WCS. If WCS slacks on defense for a minute, then in goes Koufos. Koufos IS tough. He DOES rebound. He DOES set good screens. And he IS consistent. I would also award Giles with more minutes at the forward position. He's earned some more minutes with his recent performance, both because of his offense and his defense.
I would also have Bogs come off the bench. He'll get plenty of minutes swinging behind both Hield and Shumpert. And I like that he can sit on the bench a while and Dr. Bogs can diagnose the court a while before coming into the game. I like him playing with WCS, as he's good with him offensively on the pick and roll, and hopefully he can be the on-the-court coach to get the guy to put out the consistent effort.
To really solve the SF issue, there needs to be a trade or off-season FA move, imo.