The 340 classics had a 2dB "bump" in the 80-120 Hz range. This would make them sound warmer. However, that bump was a bit unnatural and was removed with the 340 SE, which has a more linear or "flat" response.
Since you are used to listening to a pair of loudspeakers with some emphasis in a particular range, listening to a similar pair of loudspeakers without that emphasis will tend to make the frequency range outside of that emphasis sound more pronounced.
Additionally, the SE tweeter is more revealing with an extended frequency response when compared to the tweeter used in the classics.
I don't think changing the receiver from one HK model to another will make any difference in this regard. My recommendation would be to give them a few weeks. It takes a while to become accustomed to a slightly different sound. Many of our customers have directly A/B'd the SE's with the classics while going through the upgrade process and the vast majority preferred the SE's after a few weeks of side by side auditioning.
Of course, you can be in the minority and that is absolutely OK, but rather than change receivers etc., I would just give them some time
Hope this helps!