Using the pishrink.sh script ( https://github.com/Drewsif/PiShrink ) running on my Raspbian Pi with the .img on a USB hard drive I was able to shrink the subject distribution image to 4.6 GB which Win32DiskImager was able to write to an 8 GB SD.
Because the Raspberry Pi MATE distribution is network blind at first boot (by design?) and since I haven’t suitable keyboard/mouse hardware I was only able to check the boot up via HDMI to my TV to the point where it’s first input is required but it looks good to that point. If anyone wants to test it further I’ve made it available here:
https://dl.dropboxusercontent.com/u/17163211/ubuntu-mate-16.04-desktop-armhf-raspberry-pi_.img
I don’t know if it resizes to the full SD size on boot as pishrink is supposed to set up so it may be necessary to do that manually. In addition I added the -y option to the e2fsck command of the pishrink.sh script in case voluminous interaction is needed to fix up the file system.
I have to say that the lack of motivation the developers show with regard to fixing this themselves (and the network blind boot design) make me doubt the seriousness of their effort.