Mixed PPI screens

The company I work for gave me a really nice Dell Precision 5530 laptop with the really nice 4K screen option. The monitors are on my desk are your standard issue, no frills, Dell 1920×1080 screens. If I try to run all three screens at the same time (two 1920×1080 screens scaled at 100% and one 4K screen scaled at 250%) everything goes wacky. Icon and text size vary wildly. The only way to return things to normal is to choose to use only the external screens or only the built-in screen, and do the sign-out/sign-in dance. It is—unpleasant.

Has anyone solved this problem?