BAT REX 3 with Harbeth 40 series

I take it you don't have the opportunity to try the combination.  I've heard the 40.2 at a local dealership that sells only tube amplification.  This is an extremely touchy speaker that can sound soggy and lacking in dynamics and loose in the bass region with some amps, but not others, and it not necessarily the case that the more powerful amp sounded better with this speaker.  This speaker, more than most, requires auditioning with the particular amp in mind (I don't know if this is the case with solid state amps).

I heard it sound very good with certain tube amps, so I don't think it is necessarily a solid state amp only speaker. I really don't know of ANY speaker that I would call a solid state amp only speaker.  As to damping factor, this measure (8 divided by the output impedance of the amp), doesn't really matter much beyond a certain number.  I have heard amp designers say that number can be as small as 8 (output impedance of 1 ohm), and I've heard amps with substantially LOWER damping factor than that sound terrific with some supposedly difficult speakers. 

This makes it quite difficult to realistically predict how an amp and speaker combination will sound--there are no good objective guidelines. 

I have not heard the REX, much less heard it with the 40.2s, so I cannot so much as guess how that will work out.  But, I can say that an amp should not be automatically ruled out because it is a tube amp, or because it doesn't have an output in the multi-hundred watt rage, etc.  

Overall, even with the better tube amps that I heard with the 40.2s, it is not the most dynamic and lively sounding speaker--it does weight, large scale and harmonic richness very well--but it is a bit of a sluggish thing.  If I were to take a guess at to what might work best with it, I would think that an OTL amp might do the trick--something like an Atma-Sphere amp.