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"Yabbut.... seems like a bit of circular logic to me - won't I need a
height of eye value here first in order to determine the angle to the
true horizon? "

Your floating target might be something like 30 or 40 degrees down from
the horizon. Dip is only going to be a few minutes of arc, ten at the
outside, so it's negligible for this little calculation. Of course, if
you want to be extra careful, you simply run the calculation twice. On
the second pass, you add the first estimate of dip to the measured
angle. In practice, it won't make much difference.

"wouldn't it be easier to just dangle a tape measure
down to the water's edge?  :-)"

Maybe! But I've actually done this, and it works. Using a styrofoam
sighting target probably made it sound more complicated than necessary.
Find yourself a bit of driftwood. Measure its size in feet as well as
you can. Then toss it out into the water (no one will find this
suspicious). Two quick angles and a very short calculation will give
your height of eye:
ht = L*sin(B)/sin(A)
where L is the length of the target, A is the angular size of the
target, and B is the angle between the horizon and the target. Note
that if the target is a "stick", much longer in one dimension, you have
to wait to measure its angular size until it has rotated around and is
perpendicular to your line of sight.

Suppose the water is a bit too far for tossing sticks. In that case,
can you estimate the distance from where you're standing to the water's
edge by some other means? If so, you can get height of eye by a reverse
"dip short" calculation.

-FER


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