Before we go any further, please confirm that the following have been done on your pair:
1) Replacement of all worn out parts, including elastics, foam and pads.
2) Inspection of both sides of the passive radiators for tears or holes (easily done at the same time as cleaning out the old foam particles).
3) Usage of the phones on more than one system, preferably a very different design, such as a solid state amp.
For simplicity, I am going to call the early style driver "Driver A" and the later style driver "Driver B", and the early style passive radiators "Disc A", and the later style "Disc B".
This is a quick'n'dirty comparison I measured of the early (Driver A, Disc A) and middle (Driver A, Disc B) variants of the K240 a few months ago. I am not entirely sure what equipment I was using at the time, but I do think I was using a fairly bright solid-state preamp to power the phones for the measurements (rather than using my tube amp which would give inaccurate results when I tried).
The purple line is the early version, and the blue line is the middle version. They were each calibrated for equal loudness (75dB or so I think), rather than centering on a specific frequency. The response seems to fairly accurately represent how the K240 sounds to me overall, but I will not place much faith in the ability for my measurement jig to reliably measure the higher frequencies. The huge dip in 3KHz on the early version may also be a measurement anomaly, I have not bothered to retest it to see, since I do not use that version as much. In the midrange and treble, you can see the response is nearly identical since they use the same Driver A, with the differences being attributable to minor production variations, small differences in measurement position, and possibly the different passive radiators used. The primary difference is the much greater bass output on the one using Disc A, which seems to be using a thicker material for the passive radiators, so I think it is reasonable to conclude that Disc A blocks more of the backwave than Disc B, and thus increases the overall bass response.
The only way I have been able to get a K240 using Disc A to not have strong bass is by making the pads not seal properly, which is not easy to do with fresh pads. Maybe I will experiment by putting a Driver B into Disc A and see how that sounds, even though I doubt there is an early production K240 using Driver B.