... it seems a tall order to reflect such a bright image from 250mls away.
The science behind the Heliograph, or Reflecting Signalling Mirror, is well-known.
https://en.wikipedia.org/wiki/Heliograph"The range of a heliograph depends on the opacity of the air and the effective collecting area of the mirrors. Heliograph mirrors ranged from 1.5 inches to 12 inches or more. Stations at higher altitudes benefit from thinner, clearer air, and are required in any event for great ranges, to clear the curvature of the earth.
A good approximation for ranges of 20–50 miles is that the flash of a circular mirror is visible to the naked eye for 10 miles for each inch of mirror diameter"
There's no mention of this range being achieved only in darkness or twilight, so it seems the general approximation applies to daylight usage. Note that the observer sees the flash at a range far beyond that at which they could discern the physical structure of the mirror.
The principle applies to the ISS; sunlight reflecting off a reflective surface toward the observer.
All that's needed is to approximate the reflective area of the ISS and apply this approximation to calculate the range at which it could be seen from the above formula.