The issue is still very much present. We mitigated it (slightly) by adjusting the background color so that the pages are legible when loaded on devices that exhibit the behavior.
Meanwhile, we've started work on an entirely new website, rather than trying to fix whatever is wrong with this one, and while needing to give it a mobile-friendly overhaul. Anyone with HTML/Wordpress experience who would like to help in this effort is free to contact me.