Best Loudspeakers for Rich Timbre?

I have no idea what is a "neutral" sounding speaker.  That implies some kind of reference; what is that reference?  The correct speaker is the one that sounds most musical to the beholder.  It would help if the original poster would provide a personal reference of stuff that sounded good and stuff that sounded to thin or bleached of "color."  At best, I can hazard a guess that this person is looking for something from the likes of Audio Note, the O93 or O96 DeVore, Vandersteen, Harbeth (particularly the 40.2), ProAc, JM Reynaud, Trenner and Friedl, and Charney.  There are some speakers that may sound a bit bright on top that still manage to deliver weight, upper bass warms, and natural timbre (e.g., Triangle speakers).

The very best speakers, in terms of delivering saturated harmonics and timbre, to me, are horn-based systems, but these require some expertise to assemble or are quite pricey; they involve finding and using older/exotic drivers or really expensive new drivers (e.g., G.I.P. Laboratories).

If you are willing to put in some effort to hear stuff that is quite unique, check out the custom-built-out-of-vintage parts speakers at Deja Vu Audio in McLean Virginia, or at the satellite stores (Deja Vu South-Southern Florida, or Deja Vu West-La Jolla, Ca.).

Cheap components in speaker crossovers can cause serious problems with timbral accuracy by introducing distortion which masquerades as 'fast leading edge'.

Therefore suggest that you consider speakers without crossovers or delay lines. Or, consider upgrading those components in speakers of choice.

Almost all manufacturers work to a price point. Cheap crossover components are an obvious place to save - but fortunately, they are an easy thing to upgrade. I have had good luck dealing with Parts Connexion and Michael Percy Audio (no connection).

If you are good with a soldering iron, it's a lot of bang for buck. If you are on a budget, spend $10 on cables and $5000 on component upgrades instead of the other way around. YMMV

I'll throw in another vote for ProAc !

One more for Tannoy Prestige range

Spending $10 on cables would get anyone nowhere, unless you steal these cables and $10 is your taxi bill. 
It is remarkable that many don't understand that cables are components, they are equally important. Another mistake is to think that they are easier to design than electronics, speaking of high level.
How to best stretch your dollar when upgrading cannot be answered in general, sometimes it should be active component upgrade, sometimes cables or power cords, and yet at times either would be a correct path, just different.