How can I determine why keyboard response is intermittently very slow with large display?
This is a bug in Chrome as recorded at google as issue 319580.

The other symptoms as described in that bug report are that display update is very slow when the animated icon for the browser tab is on any 4K display such as the Seiki 39 mentioned in the question.  One work around is to move the browser tab animation off screen and performance returns to normal.  There is a fix forthcoming to Chrome that is available now in the Canary builds.