I've seen any number of issues running HQPlayer even when using low levels of cpu, and this with many servers. Running the highest levels of dsp available with HQP is taxing. At this point I'm pretty convinced only high level server builds using atx motherboards can run high level HQP dsp.
As for your mini, there are some guides for maximizing minis for music servers. I believe Mojo audio still has one up and running. I also have two guides I printed out back in the day when I was learning about optimization, may still be up on web. The two are from Core Audio Technology and TEWM-Getting the most out of your os x music server/player. These go into things like physically removing wifi antenna and going into DOS command for process shut downs. Finally, go to lps to power mini if you haven't already, I use Uptone MMK with JS-2 LPS. Perhaps some of these optimizations may help run HQP.
Also, are you running HQP through Roon?
And one more upgrade, certainly one of the best in my experience is bridging a second ethernet out using thunderbolt port and thunderbolt to ethernet adapter. https://audiophilestyle.com/forums/topic/30376-a-novel-way-to-massively-improve-the-sq-of-computer-audio-streaming/ This link will cover much ground in creating mini that will compete with much higher priced servers. The exact procedure for bridging will be found there. Massive improvement in title speaks for itself, not over hyping improvements here. Austinpop originator of above thread went directly from mini to Taiko Extreme, he thought modded mini that good.
With the thunderbolt as second ethernet port network will be: Router>mini>FMC>OpticalRendu>dac You're getting rid of switch and one ethernet cable with this setup. I tried audiophile switch with my setup, much preferred router directly into mini, no switch. My take is shortest network routing is best, switch becomes superfluous with 2nd ethernet port.
I don't know if any of this will help your HQP issues, but overall this will make your mini into top flight server. I will soon be comparing my fully modded mini against extreme high end atx motherboard based server with best of everything, we will see how it stacks up. This server is being built by audiophile friend with running highest level HQP dsp a priority. I myself am not convinced running any dsp, don't care for running any Roon dsp, HQP claimed to be much better.