With any luck, that promising "introductory session" will mean that this post will reach you after you've enjoyed a well-earned sleep, John...
…As it's been my experience that uncertainties like these can often rob true "performers" of their vital "shuteye" time.
...the HS30 was found to be very flat and lifeless but I think this is more down to eq settings and more time needed...
...I would suggest rolling off the extreme lows (typically below 100 Hz) for a male voice...
Not having the more comprehensive eq controls of a sound desk suggests to me that it's likely you'll need to find a very quick "tweak", should I be correct in thinking that both handheld and headset must "share" the Pioneer's simple but very effective "High, Mid and Low" controls.
To that end, I reckon that the main "clarity" issue we're facing here is most likely to have arisen from the handheld effectively having a midrange and/or upper-midrange "presence" boost compared to the "flatter" (if sometimes less "flat-tering") response of the headset's capsule.
Also, you'll easily be able to demonstrate for yourself the "bass boost" that arises from what's called "proximity effect" by bringing the handheld right up to your lips and then backing it away by as little as a centimetre or half an inch as you speak.
When properly positioned, any headset mic's capsule will nearly always tend to exhibit more of this proximity effect-induced bass (always being much closer) than a handheld, so one non-electronic form of equalisation (which, in essence, is just a fancy term for "making equal" or "matching") that's readily available is our variation to the "working" distance of each mic.
Should that not prove to be a total solution, I'd always heartily recommend (as Don's suggested) having more "work" being done by "cut" rather than "boost" through your (albeit simple) equaliser, because every bit of boost takes us closer to speaker-destroying distortion should a "burst" of unexpected loudness catch us out.
For this job, that probably means either an easy to remember (hence easily re-set) mid and top "cut" whenever the handheld's "in play", …or the application of (possibly surprising amounts of) bass cut (rather than mid or high boost) along with a tad more gain, whenever the headset's being used.
That second option may be even easier to remember and re-set, should the Pioneer console's electronics form part of the overall solution that sounds best to your ears.
I'd also like to re-emphasise the definite need to cable so as to reduce any existing RF radiation that's near radio mic receivers to the absolute minimum that's practical, as I still fear that your success yesterday may have been fortuitous, ...with your radio mics having been "on the verge" of dropping out the moment yet another source of RF happened to "walk in".