Improving my cheap DTI magnetic base

I'm sure many of you have these cheap bay magnetic base Dial Test Indicator stands:
Attachment 19997

The adjustment works reasonably well, but the magnetic base is terrible. It looks like it has been linished by hand and it very inaccurate. It wobbles on flat surfaces, meaning that the DTI needle can twitch around when the machine jogs because the base moves, moving the indicator.
I've been making it work by clamping it to help the magnet stay in place but recently I got fed up with it and decided to machine it square.

Taking it apart is easy, there are 2 screws under the label:
Attachment 19998

The switch plate drops off to reveal the magnetic which is inside a plastic cylinder. Mine looks like it has been marked with a pen at the top, and again on the block, so probably goes in one way.
Attachment 19999

Skimmed the top to get a reference surface. You can see the 2 halves joined (glued?) to a central core. I think this is a lamination arrangement to focus the magnetic field to the base surface:
Attachment 20000

Flipped it over and skimmed the edges flat. At least it can sit on flat surfaces now, but this side is supposed to also sit on round objects. As you can see it does not stand a chance:
Attachment 20001
I'm thinking about the best way to machine the sloped sides - grind a carbide/HSS tool with an angle, or tilt the vice (need to make an angle base), or make an angled shim under the part to hold it at an angle in the jaws. Will think on that one.

Flipped it onto another side. This one sits on flat surfaces, with a relief cut in the centre. Cleaned it up and made it square to the other machined sides.
Attachment 20002

Now it fits flat and square without wobbling!
Attachment 20003

Re-assembling it I added some grease to the cylinder. This has made it move smoother to rotate:
Attachment 20004

Much better, now it actually works properly:
Attachment 20006

Attachment 20005

But the label is a bit poor. Maybe I'll machine a new aluminium end plate with on / off engraved to replace the plastic end cap and label.
And the exposed steel will probably get finger prints of rust, so I'll either chemically blacken it, or hot oil it.