crosstalk is ultimately limited by the TRS jack/plug common gnd contact resistance - the simplest way around that limit is to use "balanced" wring to the headphone with 4 pins separate R,L gnd contacts - even with single ended amps
but crosstalk reduction below ~ -30 dB is just a numbers game with little audio significance - audiophile beloved phonograph playback will have bass frequency already mixed to mono to reduce groove modulation width to increase playing time, the best phono cartridges spec a vauge >30-35 dB channel separation #
Active gnd is inefficient but a possible technique when using a single V supply - the inefficiency makes using it with battery power a particularly odd engineering choice, I would consider active gnd OK with a signle polarity "wall wart" supply
the connection I find problematic on engineering principles is "3-channel gnd" where input and feedback signal gnd is separated from the "output gnd" by a the "active gnd" buffer - it is the separation of the the input and output gnds that allows avoidable errors to creep in - exactly opposite of the claims by the fans of course
I doubt "3-channel" vs "proper" passive or active gnd should be easily audible when nothing is clipping/current limiting - it is the abuse of engineering principles, incorrect measurements, claims of all sorts of audible "improvements" feeding the fanboyism around "3-channel" that I object to - "3-channel" Beta22 builds are particularly absurd, dual mono power and some Cu roof flashing will perform much better re "gnd contamination"
if you build your own then you can simply rewire the input signal gnd in simple "3-channel" amps - may require some dremel/exacto work on projects with pcb
but there is unlikely to be any "problem" with listening with either "active gnd" arrangement in well executed amps matched to the headphone's requirements for I,V, gain
as far as "coloring" the sound there is the option of adding EQ and series impedance on the output
a series R ~= Z of the headphone may give some bass boost, high frequency roll off with some headphones
tube amps often have much higher output Z than SS amps