I have the same setup as you, and use the Screens App on my iPad to occasionally manage and administrate the Mac Mini.
Screen is a good VNC App, but can feel a bit unresponsive for some specific tasks. The sluggishness of VNC solutions can be reduced when you connect your MacMini to your router through Ethernet rather than WiFi. Screens is not really the best to deal with Audirvana on the MacMini. I find it cumbersome when dealing with tracks’ metadata, or multiple selection to include in a playlist or general management of Audirvana. As for access to the slide up keyboard, I shall say no more…
After pairing, the Audirvana App on my iPad works well when just managing a listening session. I understand it is now free, it was paid for initially.
For any advanced management or “transparent” use of Audirvana on the MacMini, I use instead Screen Sharing between my MacBook and the MacMini: Negligible lag and just like working on the MacMini itself thanks to the display, keyboard and trackpad of the MacBook. Both do not need to use the same Mac OS version, so a cheap second hand MacBook may be a way forward.
If you go that way, the MacBook does not need to be powerful at all, as in this type of use, it is mostly a terminal to access your MacMini resources. Just be mindful that the version of Mac OS it comes with allows Screen Sharing.