The diodes arrived. One 1N4148 diode per switch plus one spare in case my clumsiness got the better of me.
There's a great guide on the Deskthority forum by a user called matt3o. This has been my go-to reference, so far. I followed it quite closely, but with minimum finesse. If you're going to build your own keyboard, you'll likely do a much neater job than I will.
Programming the Pro Micro turned out to be a small problem. After downloading a couple of pieces of software that each claimed would do the job, nothing recognised the Pro Micro when it was plugged in and after I did the quick, double reset to get into bootloader mode.
In the end, I switched over to macOS to use a command line utility to flash the .hex file I'd previously generated. Once I got to that point, it worked perfectly.
If you're interested, getting this done with macOS is at least as easy as it must be with Linux.
ruby -e "$(curl -fsL https://raw.githubusercontent.com/Homebrew/install/master/install)" < /dev/null 2> /dev/null brew install avrdude\
Then whilst the Pro Micro is connected via USB, but is not in bootloader mode, do:-
ls /dev/tty* | grep usb
Put the Pro Micro in bootloader mode, repeat the above command and play spot-the-difference to quickly see which additional USB TTY device shows up. Then Ninja the following:-
avrdude -c avr109 -P /dev/tty.usbmodem35 -p atmega32u4 -U flash:w:dreampad-proper.hex
Except the "/dev/tty.usbmodem35" to be replaced with the device you found instead.
I soldered the rows and columns to the predetermined pads on the Pro Micro. Everything worked! Of course, with all the keys, switches and wires flopping around unsupported, it didn't take long for some of the solder joints to come unstuck. Note to self: buy new solder and some flux. What I'm using is more than 15 years old.
Next step is to build a case. By a stroke of luck, where I work I have access to a laser cutter, 3D printer and CNC router.