Unable to set 2560x1600 resolution to Apple Cinema Display 30" via Apple Mini-Displayport to Dual-link DVI adapter on 2013 Macbook Pro 13"

I'm trying to revive a dusty old 13" MacBook Pro Early 2013 (Model A1425, 2.6 GHz i5) by installing Ubuntu (20.04 or 21.10, Lubuntu/Xubuntu/Ubuntu-Mate) on it.

I have two 30" Apple Cinema Displays, which should run at 2560x1600 over a Dual-Link DVI connection. I also have two active Apple Dual-Link DVI to Mini-DisplayPort converters. This setup works perfectly when plugged into my 2015 15" Macbook Pro running macOS.

When I plug the Mini-DisplayPort connectors into the 13" MBP running Ubuntu, the only resolution I can pick in the display settings screen is '1280x800*'. The image has 1/4th the resolution of the screen, but it is stretched out over the full display. I'm not sure whether this has anything to do with the Dual-Link-ism... (I believe the screen is physically divided in two halfs for either DVI link?)

The screens do work when running macOS, which I reinstalled to verify; see the screenshots in this Imgur post.

Intel HD Graphics 4000:

  Chipset Model:    Intel HD Graphics 4000
  Type: GPU
  Bus:  Built-In
  VRAM (Dynamic, Max):  1536 MB
  Vendor:   Intel
  Device ID:    0x0166
  Revision ID:  0x0009
  Metal:    Supported, feature set macOS GPUFamily1 v4
  Displays:
Colour LCD:
  Display Type: Built-In Retina LCD
  Resolution:   2560x1600 Retina
  Framebuffer Depth:    24-Bit Colour (ARGB8888)
  Mirror:   Off
  Online:   Yes
  Automatically Adjust Brightness:  No
  Connection Type:  Internal
Cinema HD:
  Display Type: LCD
  Resolution:   2560 x 1600
  UI Looks like:    2560 x 1600
  Framebuffer Depth:    24-Bit Colour (ARGB8888)
  Display Serial Number:    CY6230AEUG1
  Main Display: Yes
  Mirror:   Off
  Online:   Yes
  Rotation: Supported
  Adapter Type: Apple Mini DisplayPort To Dual-Link DVI Adapter
  Automatically Adjust Brightness:  No
  Adapter Firmware Version: 1,03
Cinema HD:
  Display Type: LCD
  Resolution:   2560 x 1600
  UI Looks like:    2560 x 1600
  Framebuffer Depth:    24-Bit Colour (ARGB8888)
  Display Serial Number:    CY7171G8XMP
  Mirror:   Off
  Online:   Yes
  Rotation: Supported
  Adapter Type: Apple Mini DisplayPort To Dual-Link DVI Adapter
  Automatically Adjust Brightness:  No
  Adapter Firmware Version: 1,03

I've spent a day searching and trying different xrandr commands, but so far I've only managed to completely 'black out' a screen and to get a bit of a 'vibrating' bad-looking image, at 2560x1600...

Behavior is the same for Ubuntu-Mate, Xubuntu, Lubuntu. But when booting from a Linux Mint Live USB, I managed to get one of the screens to run at 2560x1600 for a couple of seconds, before everything went back to low-res randomness again. I also don't understand the behavior of the Display layout screen; the monitors jump to different positions and randomly start to mirror...

Any suggestions on how to get this setup running?