"What are the EXACT characterists of a 6550, 88, 90?"Wrong question. I have tried a few brands of new production 6550's and KT88's in my VTL's, and each kind sounded different. As anybody with a little tube rolling experience can tell you, there is no "one sound" for each tube type -- different versions with the same model designation are not physically or electrically (and hence sonically) equivalent, and that includes different brands, factories, and vintages.
I'm also not sure that your amp, apparently designed to use KT90's, is really a good candidate for KT88's as drop-ins. For instance, I know that my amps, which come stock with 6550C's, can't use KT90's without resistor changes, although KT88's are fine. And if your amp uses autobias, there may be no way for you to tell if the replacement tube type is not being biased in the proper range by a circuit not designed for it.
FWIW, in my amps a swap from SED 6550C's to EH KT88's produced improvements in essentially all the same areas you're complaining about, and the overall effect would be outstanding for a classical listener in my view. But although my speakers are also about 87dB sensitive, my amps are ~200w, and obviously everything else is different too. BTW, when comparing tubes you must make sure one set isn't wearing out, or still breaking in -- that will totally skew the results as well.