First I think you mean DT880's which are the neutral sounding Beyers. I would honestly keep away from the 600 Ohm unless you have heard all three versions side by side. Why chance introducing a hard to drive headphone into your setup. I use the DT990 ( 250 Ohm ) and really like it and have my own reasons why I chose the 250 Ohm version.
At the $1200 range you can really enjoy some nice gear. Some simply options are listed below as alternatives to your listings.
1.) CEntrance DACport @ $400
Great DAC with good to great specs including output impedance, THD%, and SNR
2.) HeadRoom Desktop Amp $ 850
Has a built in DAC and the headamp section is top notch. I still prefer the Ultra Desktop, but it is slightly outside of your budget.
Those are devices I am familiar with and would recommend at the below $1200 mark. You could also look into the Headroom Micro Stack which provides you with both a DAC and headamp separately. Together they take up very little room and sound very nice together.
I have seen a few posts about Lyr products that are not necessarily good ones. I do not have any personal experience with them and perhaps someone could chime in here comparing a Lyr to another DAC/amp that they have listened to. I try not to provide conjecture or accept any either.
Looking at the Woo WA6SE's numbers there is a poor THD spec at or below .3%. For example the Desktop Amp has a THD of <.002% which just crushes the Woo. The Woo also has tubes which introduces the need for repair later on when they wear out. A solid state amp will serve you well for your entire lifetime.
The same goes for the Lyr. The THD is only .1% or below with tubes. Yet again another part lurking to fail. Regardless of the 5 year warranty you want to go by specs or at least listen to both prior to finalizing your decision.
