You might as well just go with the simulation. Either way the original signal will be modified, might as well use what you have that you already like than gamble on tube amps. OTL amplifiers that perform as intended (regardless of the sound modification it's tuned for) on high impedance loads are wildcards on low impedance loads (ex Little Dot MkII can make Grados sound thicker but AKGs sound more like tin cans), so unless you're using an HD600/650/800 and the like, ie everything with 250ohms and up, you might end up with the exact opposite sound out of every colorifying boombasticator you try. Might as well EQ or colorify and boombasticate at the digital level then run the signal through a clean analog handling process (ie a good, clean amp, or use a high sensitivity, not too low impedance IEM so as not to tax the audio chip on that smartphone).
At the same time note how OTL tube amps are actually for the better amps actual amplifiers and not much colorifying boombasticators. Their job is still primarily to amplify the signal with as little modification as possible, and if anything, they're designed to deliver a lot of voltage at high impedance. The Schiit Valhalla is a prime example of that - mostly unmolested sound on high Z headphones but rough edges in the recordings or the 3500hz and 6500hz peaks on the HD600 are slightly smoothened out, while you get as much of the "impact" at the low end that isn't really boosted but comparable to what you'd get out of a Lyr or Asgard for example.
I am using the HD650 headphones. This is a great post btw.
That Little Dot MK2 looks interesting, I'm not too sure about the comparisons between different tube amps, I know nothing about them.