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@YouSir56922
So curiosity got the better of me and I bought two 105 cassettes from Merlin for just over £40.
I can confirm that it is definitely possible to assemble a semi-custom 12-28 in the manner that I suggested.
However, the cogs used in the 12-25 and the 11-28 are not identical. They carry an alphanumeric designation relative to the number of teeth and the exact design.
So on the 12-25 the 17T cog is called "17A", and on the 11-28, it's a "17B" or something like that. The difference appears to be the positioning of the teeth relative to the splines.
Anyway I assembled a 12-28 with the 17T cog from the 11-28 as this just looked better (unscientific), and gave it a go with the bike in a stand. It worked and shifts across the cassette in both directions with no discernible difficulties.
This cassette is probably sub-optimal since the positioning of the teeth is not the same as on an "out-of-the-box" one, but given that it seems to work, it is almost certainly better for me than one which gives me a top gear of 52x11 which I will hardly ever use.
If my cassette/chain/hub/wheel/bike/face explodes from the use of this deviant equipment, I will be sure to post an update.
TLDR - cheap Shimano 12-28 11-speed. Works.