That sounds like an unusual arrangement for a Stax amp. Bypass its internal preamp with an external one? There is no such preamp stage in most direct-drive Stax amps, which need to supply 50 - 60 dB net gain (more similar to phono stage, minus the EQ). I guess you could bypass the volume control, or perhaps you’re dealing with a design that puts traditional pre & power amp stages before some output step-up transformers to supply the needed gain.
Anyways, you can’t go wrong with the ARC Reference 6 or 6SE. They’re fantastic. Or a VAC Signature (used) if you want more midrange sweetness. I’ve tested both (well, a VAC Master in my case) feeding headphone amps, and yep they sound great. I also had an RP-9, and it has a leaner midrange with less sweetness than the ARC and VAC. Though I did also try the RP-9 feeding a headphone amp, and it can indeed work well too - nice punchy bass. The Ref 6 and VAC have a lower noise floor than RP-9. There are reasons they cost more.