As delivered from Kenwood, the '940 incorporates a Murata CFJ455K-12 filter in the SSB transmit signal path. This filter has a 6dB B/W of 2.4KHz. The rig sounds "good".
It is a fairly easy proposition to widen the TX B/W up slightly (to 2.8KHz) and make the rig sound "great", all the while keeping the audio narrow enough to be neighborly.
Three ways to accomplish this:
1) Find a surplus CFJ455K-13 filter (eBay, private sale, etc) - $$$
2) Go to a Kenwood parts distributor and hope they still carry one - $$$$
3) Wait for a used TS-930S "signal board" to come up for sale then snatch it.
I opted for Item 3 - twice. My average price for one of these boards (complete with filters) is $70. Desolder the filter and swap with the one currently in your '940. Voila! Done.
Your '930 board should also have a YK-88S2 SSB filter installed. Desolder and swap it with the '940's YK-88S1. Your rig's SSB receive B/W will now be 2.7KHz instead of 2.4, and can be "tightened" as before via the Slope Tuning controls. This filter is selected on AM when one presses the 'NAR' switch. The wider filter results in easier copy of an AM signal but is still an effective QRM fighter. It's also much more pleasant to listen to than the stock SSB filter.
Easy, wasn't it?