Best coffee maker for brewing konacha?

I’m a fan of fine gyokuro konacha. For convenience, I like brewing all my day’s tea (20 g) in one go, and pouring it into an large insulated bottle. Konacha has a lot of dust and, to minimize the amount that gets into the tea, I pour it through two ultra-fine stainless steel filters; the first is 50 microns, and the second is 30 microns.

The problem is that, even with those, some dust gets through. That’s not a problem for the first few cups I drink but, as the day progresses, the dust that’s left continues to steep, causing the tea to become bitter.

I tried pouring it through a coffee filter, but that doesn’t work, because it just clogs the filter and I get no flow.

So I was wondering if I could use a coffee maker that employs pressure to force the water through the filter, thus giving me a cleaner brew. Some do use coffee makers for brewing tea, e.g., https://www.teabloom.com/blog/best-ways-to-brew-tea-in-a-coffee-maker/

Any suggestions on what models might work? Or better yet, anyone have experience doing this?

I’d considered a French press but, according to Wikipedia, that design is unsuited for fine particles, which is exactly what you find in konacha: “Finer coffee grounds, when immersed in water, have lower permeability, requiring an excessive amount of force to be applied by hand to lower the plunger and are more likely to seep through or around the perimeter of the press filter and into the coffee drink. Additionally, finer grounds will tend to over-extract and cause the coffee to taste bitter”. [ https://en.wikipedia.org/wiki/French_press ]