HEPA simply means High Efficiency Particle Absorbing. To meet a true HEPA classification, the filter needs to remove 99.97% of particles that 0.3 microns across. They are actually even more efficient at particles larger and smaller according to wikipedia - the 0.3 micron size being chosen as the reference simply because it is the hardest to capture.
https://en.wikipedia.org/wiki/HEPA#History
Basically, the material is made of very fine fibers in a random arrangement, and the tiny particles bump into the fibers and get trapped by static cling. It does not sound like vacuuming them out will help much, and washing actually makes them worse:
https://smartairfilters.com/en/blog/how-to-clean-wash-hepa-filter/
If the air purifier is doing a critical job, then you will be best served with a scheduled replacement of your filter. Could there be a way to mitigate the problem that the air purifier is solving? Selling your house and moving to a state with better air quality might not be cost effective compared to those filters, though :)
You might also look into electrostatic precipitators, which are filter-less, but I think they have their own drawbacks.
Finally, a DIY true HEPA is likely going to be a very tough project, but you might be able to cobble something together that is good enough. I would start with researching world war 1 era gas masks, which probably used the closest thing you will find to sustainable materials for a high efficiency filter. Let us know if you find anything interesting. Wildfire season will be here before long...