if there is a speaker that is a worthy competitor of electrostatics and planar/magnetics/ribbons, with respect to reproduction of timbre, using "conventional" drivers, i would want to audition it, unless i have already heard it.
Ok - but it isn't an issue of timbre. Gordon Holt used the big Soundlabs for many years - he now uses ATC SCM 50 actives - I suggest you start there. I expect the radiation pattern and room interaction will still be quite different from the big Soundlabs, however, the "TIMBRE" of both is of very high quality.
I suspect you may not be able to get past the differences from room interaction / reverberation and sound field from a short listening session (you have preconceived expectations). However, if you were to acclimatize and give it a few hundred hours then you might think differently. Leading classical audio engineers certainly do not have a problem with the timbre of these cone speakers, however, I would add there are many other good cone designs too....if you took the time to acclimatize I think you would find there is not such a "great divide" as you insist.
Are all tubes bad? Are all SS amps bad? Is all CD redbook sound bad? Is all vinyl inherently bad? Is all 5.1 HT sound bad? Is all two channel music bad? Are all horns bad?
IMHO - NO.... all of the above can sound excellent... given the right choices and room setup.