The typesetting adventures continue.
After a couple of hours of tinkering with the (surprisingly few) public GUI-based font subsetting tools, I've come to realize that the only reason my results up until this point were so subpar was because of a single tiny feature I'd always neglected for its seeming lack of necessity.
Long story short: I've managed to make the main font of this site, called Inter, significantly smaller in size but also not janky in presentation.
Which is the biggest problem I've had so far in trying to tame this typeface: it's either pretty but full-size (100kB+ is no joke, mobile or not), or awfully-pixelated but slim.
Given that there are very few publicly-available non-command-line subsetting tools out there, I was limited in precisely what I would be able to tinker with. (Even if you don't know what you're doing, messing with digital tools may eventually produce the desired result if you're patient.) So far, I've been using Transfonter for some light subsetting (i.e. when I only need to reduce the amount of glyphs per font file), and FontSquirrel's Webfont Generator for anything more robust.
The latter has a small feature called "Fix GASP Table". The "GASP" in "GASP table" stands for "Grid-fitting And Scan-conversion Procedure". The table itself is used in deciding how to render said font within a greyscale (i.e. black/white) device.
How this relates to rendering on a webpage – of this font or of any other – is beyond me. All I know is that I was able to make significant progress towards making the site a lot less crappy for users with limited connection speeds or data plans.
(Interestingly, and for reasons beyond me again, this makes the rendered font thinner. If you have Inter installed on your device, it will look noticably better than if you use the site-supplied slim version. If you can help me solve this mystery and render the fonts both desktop-grade-pretty and slim, contact me.)