One thing I did with my 10"er was to make sure the two struts had a long clamping area, if that make's sense. If the struts are just "pinched" in place, they will not hold their square securely.
The whole length of the mirror box holds the struts in place, and the cage also has long grip.
I think this is important for small numbers of struts, without resorting to 'string' setup. This is the compromise mechanically. I could be wrong

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The increased bracing I was thinking of may be through the clamp coupleing of the struts, and an extra ply planel behind each alt bearing.
I could just be blowing smoke!
The cage also would require larger clamping area. These could extend down three or four inches.
This Sonotube OTA has been reworked already. Have to reconsider its viability in this project, and not be so romantic.
Mental.