One reason for the problem may be this.
You can see that the mids and HF units are over attenuated at the 800 Hz crossover point. In addition BSC seems on the over generous side.
A speaker with an FR like that will sound over warm and appear to have a strong bass, when in fact the F3 is 49 Hz.
Now I suspect that Audyssey is pulling that 5 db or so rise below 800 Hz down. The OP does not like that, as he likes the speakers the way they are.
In addition his receiver only have a 6 ohm rating. His speakers are quite definitely four ohm. So it is possible his receiver being a newer vintage does not handle that the best. With the FR the way is is, you know those speakers are going to be pulling a lot of current and increasing below 800 Hz.
This may actually be the crux of the matter.
As I have said before there are just too many power amps in receivers. They need a diet of 5 max. If people want more channels then there needs to be a forcing to use preouts and use external amplification.