The way I read Dan's post (and I might be mistaken) is that he wants to use the KX-5 to control the K4, and wants to be able to transpose while doing so.
But the KX-5 doesn't have any buttons for transposing-- just for shifting up or down one or more octaves at a time-- so he's using the transpose function on the K4.
But when he does that, the K4 keeps playing whichever notes are being sent from the KX-5, with no transposition being applied by the K4 as hoped.
If I've understand the scenario correctly, I think the problem is that the transposition of the K4 is only for changing the note values of the keys which are pressed on the K4, not for changing the note values of received Note On/Off events. But there may be an option to apply the transposition to the received MIDI data.
Looking at the PDF of the K4's manual (which, unfortunately, isn't searchable since it's made up of scanned images of the paper manual), there are two entries related to transposition in the index:
TRANS (MULTI MODE) 64
TRANSPOSE (SYSTEM) 14
Dan, until I hear differently, I'll assume that you're using the SYSTEM TRANSPOSE as described on page 14, which apparently affects only how the keys you press on the K4 itself are interpreted by the K4's sound generators.
Looking on page 64, it sounds like the MULTI MODE TRANS might do what you want, since (I assume) it's for transposing different parts of splits and layers regardless of the keys being pressed on the K4-- i.e., the key that produces a note value of 60 (Middle C) is going to continue producing that note value (unless perhaps you're also using the SYSTEM TRANSPOSE), so each part (layer or split) that responds to that particular key is going to transpose the note value of 60 to some other value. If that's the case, then I would expect it to also transpose any notes received via MIDI.
However, if that doesn't work, page 64 has a note that refers to page 46 and whether the DCO KEY TRACK option is turned ON or OFF. So I would recommend leaving the SYSTEM TRANSPOSE set to 0 (unless you plan to play the K4 using its keyboard in addition to playing it remotely via the KX-5), and either use the MULTI MODE TRANS with the DCO KEY TRACK turned OFF, or leave the MULTI MODE TRANS set to 0 and try using the DCO COARSE setting (described on page 46) to transpose the sounds produced in response to the note values of the MIDI Note On/Off events.
[Original post edited slightly to try to improve readability.]