bass. over-ear. $200 - $300 budget for two… $400 - $600 for the third.
one has good sub bass.
second has good mid bass.
third does good on both.
and it’s actually six. three open back and three closed back.
what would you recommend considering for DAC and Amp with a budget of $500 - $1000 for both?
I would definitely suggest just one pair of open and one pair of closed of drastically better overall quality than 3 turds of each. Give those HE560s a chance, let me send you a pair of grills and pads too. If you have the amp to drive them, they take bass EQ like crazy and the pads and grills alone will significantly increase the lower and sub bass. They can slam seriously hard.
ah… daft I am. two missing buts of info most definitely needed to give context.
1 - these would help train me to recognize what good sub and mid bass sounds like.
2 - examples of different genre’s of music that exemplify sub or mid bass as well as both at the same time.
are you trying to test the quality of the music or the quality of the headphones?
the sound, feel and presentation of both types of bass performance.
I guess I could consider one open and one closed that do both well and use the music to exemplify and reproduce sub / mid bass characteristics. 
Sub bass, mid bass… I would try Beyerdynamic T1 3rd gen in your place. Easy to grab ~40% off used.
thank you for the suggestion 