To be clear, I'm not suggesting these two purchases are complementary - I know planars are a poor match for OTL (though weird coincidences do sometimes occur).
I have a set of DT-880/600 that reputedly are a dynamite pairing with the BHC, and if I buy the Tres, my existing HO200 amp should fit the bill.
Yes, sometimes that rule is not a hard one. The AKG K701 is dynamite with the Glenn OTL despite being a low impedance headphone, and supposedly the old HE500 is a good match on the La Figaro 339, but generally speaking it's not a good idea to use planars and/or low impedance dynamic driver headphones with an OTL.
I have the DT880 600 ohm version and as you mentioned, that is a prime candidate for an OTL amp. Questions though, are you a fan of the way the DT880 sounds, and what is it you're hoping to get out of a DT880+BHC pairing?
IMHO, you'd be better served getting a tube amp that you can use all of your headphones on as opposed to an amp that will only play nice with the DT880.
I've owned the Woo WA2, La Figaro 339, Glenn OTL and now the Airmid OTL. Owning an OTL is a commitment and you are extremely limited as to which headphones you can use on an OTL.
ZMF headphones for example, are worth building a system around as they scale incredibly well, but the DT880 will remain bright and bass light regardless of which amp you're using.
I've not heard the planar you're considering so I can't offer any advice there, but unless you absolutely love the sound of the DT880, it isn't worth buying an amp just for it.
Just my .02