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Greg R. (#1) you wrote:
"Yeah, that was my original thought too - since the visible horizon is only
a few miles "out there" the state of the tide should be pretty much the same
there as at the shoreline..."

Yes.

And you wrote:
"...but the flaw in that argument would be what I said earlier, that the
measured shoreline elevation would depend on the level of the tide at the
time. And if it were in some location that had a much higher daily variation
(say 10' or more), that would definitely be enough to affect the He
correction"

Yes, if you get the height of your location from some other source (like a
survey), or you measure it once when you first discover your favorite
sight-taking spot and then forget about it. Myself, I usually just walk over
to the water and look. I could imagine this issue could cause some confusion
if you're taking sights once a week on your lunch hour... this Tuesday, it's
high tide, next Tuesday it's low tide, the following Tuesday, high tide
again... You could easily get a "mysterious" fortnightly "error" of 2 or 3
minutes of arc.

And:
"(seems like it works out to about a minute for every 3 feet or so of He at
these "low" levels - don't have an almanac handy right now)."

When you don't have a table or reference with the right formula handy, the
best short rule to remember is "dip is square root of height of eye in feet"
(example: height of eye = 25 feet, dip = 5 minutes of arc, nearly). And, not
by coincidence, the distance to the horizon follows a similar rule,
"distance to horizon in nautical miles is square root of height of eye in
feet, nearly."

 -FER
http://www.HistoricalAtlas.com/lunars

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