Dear Chris,
I am looking at the numbers for the definition of one knot.

If 1 knot means 1 nautical mile per hour, then the value of 1 kt is
1.687811... ft/s, since there are 3600 seconds in an hour and 1 nautical
mile is 6076.11... feet.

Now, for the practical reasons you have laid out ropes with knots were
used that had a length much less than a mile. In the dictionary entry I have
found on the internet and sent to you it is clear that two definitions of
the knot in terms of rope lengths circulate, namely 50 foot between knots
and time interval 30 seconds, or 48 feet (8 fathoms) and 28 seconds. If you
look at these two speeds you find that neither is equal to the exact value
above:

50 ft/30 s = 1.66666 ft/s or 1.25% from the true value
48 ft/28 s = 1.71428 ft/s or 1.56% from the true value

Therefore the use of the 28 second timer seems bizzare as you have noted.
Perhaps it was chosen because it did at least allow the use of the 'popular
unit' 8 fathoms (48 feet), even if it ment being 1.56% away from the true
value.
In terms of physical measurements and the reasonable accuracies one can
achive using sand timers, eye measurements and so on whilst standing on a
heaving deck in the rain I would say that the loss of accuracy in using 8
fathoms and 28 seconds can be ignored.
So, I am leaning towards the 'explantion' of the 28 second timers that 8
fathoms was a much used number for length measurements and that this
overrode the choice of the time interval. If an exact speed was required the
eact time interval to require if 8 fathoms had to be used for the distance
would be 28.43 seconds. I think the manufacture of sand timers is so
inaccurate that being off by about half a second in 28 seconds is beyond
practical requirements and that the timers were just called '28 second
timers'. They were perhaps manufactured to exacting standards and were close
to 28.43 seconds....but I doubt this. Measuring fractions of seconds
hundreds of years ago was NOT something a glass-blower fussed about.
One might speculate that sand timers were produced in large numbers to
approximate specifications and then tested with exact clocks and only the
best timers selected for sale for naviagtion purposes. This leaves open the
possibility that '28 second timers' are in fact close to being '28.43 second
timers'. If salty naviagtors worried about the .43 seconds in namingthe
instrument I doubt very much....

What do yok think Chris? Problem solved? 28 seconds is simply the
nearest integer number of seconds if you 'must' use the distance 8 fathoms
or 48 feet.

Cheers,

Peter