You are bound to be just as frustrated for the next 10 years until you learn this:
Tinycore is a TOOLKIT, and NOT a distribution!
The devs provide the tools, and if something doesn't fit your needs, *YOU* are expected to forge custom solutions from those tools. Possibly share. They don't owe us anything. And they aren't expected to be linux-teachers from bare metal upwards either.
That being said, as a user of both AntiX and MX-linux myself, and based upon your many needs, I heartily suggest you continue down that path. Since AntiX is based upon custom window managers that you don't like, I suggest you skip that, and go directly to MX-Linux that has a more modern DE desktop environment as standard.
Thing is, have you actually *tried* them, or are you just reading back bullet-points?
So yes, make it your new-year's resolution to try MX-Linux for real.
As for all the *core's - they are doing exactly what they set out to be, a toolkit and not a distro per se, which sets them apart from all the rest. Apples and Oranges. There is no "competition" here.
Seriously - take the MX pill. You'll feel better.
Badgering TCL to be something they aren't for another 10 years is not going to be productive. You've answered your own question really - AntiX or MX is in your best interest.