IMO opinion always upgrade in this order: hp>amp>dac. So I wouldn't worry too much about the dac unless you are having jitter or playback issues. I have owned several of the LD amps and the lyr is much better to my ears. I have not owned any of the others that you mention although I hear that the Woo stuff is very nice. The lyr has curbed my appetite to get newer amps. It's just a beast of a pairing.
I though tit was in the exact opposite order
I upgraded my dac once and it actually made me go from despising a HP/amp combo to kinda liking it (amp still wasn't my taste but it was a lot better still). Then again, it was from a FiiO E7 (~$100) to a PS Audio DLIII (then retail $800, $500 used). I think if you want higher quality sound (not a SS change) and your headphones aren't obviously the limiting factor an amp or DAC upgrade may be good to try first. Especially with the 650s ;)