I’ll come at this from a different angle …
What’s that then? Do you mean the Sennheiser EH350?
Since these are basically all significant distortion generators (by design) of some kind, I wouldn’t go overboard on anything feeding it in terms of initial fidelity. Any of the commonly recommended $100 DACs is going to be more than sufficient (and almost certainly measure better than the output from the simulator).
Buying audio-electronics with the intent to maybe utilize a capability in anything less than the very-near-term, usually means you’re spending money for nothing. Good chance something better will come out closer to when you need it, and if not prices on things that are appropriate will probably fall.
I can’t think of anything for under $500 that is going to make a meaningful difference to what you have already except, possibly, with your IEMs (and that’d depend heavily on what you have).
You’d almost certainly do better either getting another iFi Nano (since you seem to like it), or a $200-ish desktop-stack (Modi 3/JDS labs Atom etc. see posts starting here), and spending the other $300 on better headphones.
MQA-options at the prices you are talking about come down to iFi Nano and Micro iDSD BL, Audioquest Dragonfly Black and Red and the Meridian Explorer 2 (the only full-decoder here).