Is the actual measurement known, of the height of the Matchbox transformer?
Or does anyone have a good shot from the top, showing the two arches / half circles?

* Looked at every thread with the word "transformer", but came up empty.

The section to cut off is 15mm according to hyperdynelabs build guide.
http://www.hyperdynelabs.com/mt/construct/o.htm

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Noted thanks I'll be remembering this.

One point to keep in mind is that the Kango body is curved, so a straight cut across the transformer will not work, without leaving gaps on the sides.
Cut the piece larger than needed, leaving enough material to shape the edges down to finished height.

If you have the Hama timer already attached, it makes a good depth gauge to judge height distances, between it and the transformer, when looking at the production photos.