i3 and highdpi / HD dual screens: how to scale properly?

I have two monitors:

DP-1: 1920x1080 (hd, secondary)

eDP-1: 3840x2160 (4k, main)

My problem:

I want to set my 4k monitor to 200% scaling @ 3840x2160, and my HD monitor to 100% scaling @ 1920x1080

What I have attempted:

Running i3, it appears, visually the default setting is to keep everything at 4k @ 1x1 scaling. (When I check arandr it appears the HD monitor is set to 1080 but visually this does not appear to be the case).

In the gnome desktop environment, I must do a bit of trickery to get my two monitors to display properly. I run: xrandr --output eDP-1 --scale 0.999x0.999 --pos 3840x0 ; xrandr --output DP-1 --scale 1.999x1.999 --mode 1920x1080 --fb 7680x2160 --pos 0x0

In Gnome, that works like a charm, but when I run this in i3, it appears to set everything to 3840x2160 @ 100% scaling (very very small). I also get the error:

X Error of failed request:  BadMatch (invalid parameter attributes)
  Major opcode of failed request:  140 (RANDR)
  Minor opcode of failed request:  7 (RRSetScreenSize)
  Serial number of failed request:  33
  Current serial number in output stream:  34

What I've done:

✔️ I can make the HD monitor work as follows: xrandr --output DP-1 --scale 1x1 --mode 1920x1080

Now when I adjust my main 4k monitor, it has the following curious behaviour:

✔️ xrandr --output eDP-1 --mode 3840x2160 adjusts it to the right resolution

❌ xrandr --output eDP-1 --scale 2x2 makes it REALLY small

✔️ xrandr --output eDP-1 --scale 0.5x0.5 makes things the right size, but blurry

❌ xrandr --output --dpi <attempted with value 96, 192> doesn't work and fails with:

X Error of failed request:  BadMatch (invalid parameter attributes)
  Major opcode of failed request:  140 (RANDR)
  Minor opcode of failed request:  7 (RRSetScreenSize)
  Serial number of failed request:  33
  Current serial number in output stream:  35

So I am able to have both monitors at the correct resolutions, but I am unable to have crisp 200% scaling in my 4K monitor. For some reason where I had to do 2x2 scaling in Gnome to make things bigger, I must do 0.5x0.5 scaling in i3 to make things bigger, and this makes it blurry. Edit: oh yeah and although the UI elements are proportional, the mouse is REALLY big

Through the centuries I have since figured this out. The solution is not to apply 0.5x0.5 scaling, but to adjust the DPI. I didn't think the DPI adjustments were working because you need to refresh i3 to see them (Mod+shift+r)

I added the following to ~/.Xresources:

Xft.dpi: 192

I then ran the following commands:

xrdb -merge .Xresources

exec i3

I then ran the following script, borrowed from [this article][1]:

#!/bin/bash
xrandr --dpi 192 --fb 7680x4320 \
    --output eDP-1 --mode 3840x2160 \
    --output DP-1 --scale 2x2 --pos 3840x0 --panning 3840x2160+3840+0

After that the scaling seems to work! [1]: https://blog.summercat.com/configuring-mixed-dpi-monitors-with-xrandr.html