Having recently tried the filtering thing, it’s still a roll of the dice unless you’re using the much more expensive professional grade filters.

It does get your mead clear as hell though, and removes a ton of off flavors.

I’m no expert, been doing it as a hobby for about five years now, but from my own experience I’ll make a few notes:

• Be prepared to wait for your mead to age out, especially if you go high ABV and pure honey with no additions. If you want fast turnaround do sweet, low ABV meads or make beer instead.
• Time forgives all sins. If your mead tastes like ass, simply wait long enough and it’ll probably taste great. Sometimes that time frame is 2 or 3 years, but it’ll (probably) get there eventually. Rack into a new vessel every once in a while as long as you’re seeing sediment collect at the bottom.
• Adding nutrients, especially adding it in steps during primary, makes a huge difference. As in, being able to drink your mead in 4 months rather than a year+. I’ve found the easiest way to do it is with Fermaid O and the TOSNA Calculator. There are more complex nutrient calculators out there if you want to get deeper into the math.
• I’ve also started adding O2 during primary fermentation, although I started it around the same time I started using yeast nutrient so I can’t really tell you how much of an impact it makes.
• I’ve personally found that doing one gallon batches just isn’t worth it, for all that I see it commonly online. Unless you’re doing low ABV mead, it’s going to take time to age out into something nice. At which point if it’s good, you’ll be disappointed you didn’t do a larger batch. It takes more setup equipment and 5+ gallon glass carboys are pricey, but if you have a local homebrew store getting a basic fermentation bucket (often found in beer homebrew kits) is very worth it. That also goes with getting actual airlocks which are cheap enough that I think it’s worth picking up to take less risks with your mead
• See if you can get your honey locally, and if they’ll cut you a deal on buying in bulk. If you can’t, webstaurantstore.com has surprisingly reasonable prices for delivering 5 gallon buckets of honey.
• Making your wine sweeter is a good way to make it taste good faster without having to age as long, but do give dry meads a try! They’re very nice!
• I have filtered mead (using basic plate filters and gravity), and it improved the taste and clarity more than I was expecting. No idea how successful it was at stabilizing it because I didn’t backsweeten afterwards. From my research, if you want 100% guaranteed stabilization from filtering you’re looking at some pretty expensive equipment and filters. By the same token the science behind chemical stabilization as talked about in the OP is not as cut and dry as I was hoping, so I don’t know that there are good guarantees anywhere for this.
• Edit: Do research first if you want to attempt a bochet. Boiling honey expands to 3x the original volume, and superhot molten sugar is one of the most dangerous things you can have splattering around in your kitchen!