UPDATE:
1. I tried the Proxxon MF70 Micro Milling machine with the tool with the 45° cutting edge
("Busch Burr Stone Setting 8.0mm"
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Although yes, it DOES work on my 1mm thick steels, it's a struggle. I set the speed to its minimum (5000rmp). It takes about 5 passes and it makes rather a mess of the job. Making it work harder, can certainly slow down the cutting speed but it doesn't improve the quality of the cut and doesn't really speed anything up.
[Passing comment: It feels odd not getting any feedback for how much strain the machine is taking, other than sound… plus a slight flexing!]
2. I also bought that cheap disk + belt sander from Aldi (Ferrex), partly because I found a couple of favourable reviews.
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It's huge beast of a thing… much larger than I really wanted but it's certainly cheap (£93 delivered).
But I have to say the build quality is appalling! The hole for the rod that supports the worktable rod was way, WAY off being parallel to the disk. So far off in fact that it was physically impossible to get the work table square to the disk. Unbelievable. In the end I did some hard-core filing down of various key components and just got there.
Having got everything set up, one problem is that the sanding disk is of course mounted on velcro and so grinding a precise amount off is hard.
i.e. If you move a part onto it to a fixed, pre-set position, it seems to carry on grinding for an eternity but taking less and less and less metal off.
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[The green arrow shows the small amount of the original face that I am deliberately leaving.]
Of course if you want to speed things up you can just move the part more deeply into the path of the sandpaper, and limit the depth of the cut by the TIME you leave it there.
Yes, this approach does broadly work, although the sand paper starts slightly bending around the part, and the cut face is no longer very flat!
But it's good enough to take the parts to my diamond whetstone to finish off.
Anyhow, thank you @JasonB for the inventive configuration.
PROBLEM SOLVED 
P.S. The build quality of the Proxxon was pretty poor too. Did I mention that one of the 4 little screws to hold down the milling table simply could not be screwed in AT ALL. Luckily I found a spare old bolt with a thread that matches… but honestly!