plural possessive question

[Bill Troop billtroop@xxxxxxxx]

May I pose a question to the grammarians on the list? I am one of those who
strongly cling to the convervative view that nearly every plural possessive
must have an apostrophe-s (i.e., CBS's, etc.). It sets my teeth on edge
whenever I see an exception to this, usually in the New York Post or some
other tabloid, and it distracts me beyond endurance when this artificial
locution actually finds it way into speech. My question, or rather my
several questions, have to do with the New York Court of Appeals and the US
Court of Appeals of (for example) the Second Circuit.
Is it proper (and consistent with the principle expressed above) to write,
"... the New York Court of Appeals's most recent discussion of vicarious
liability in ..." ? Somehow it doesn't sound quite right.
Should the s be dropped in this case? Would this be an exception to the
general rule? Or should the s after the apostrophe be retained at any cost?
Similarly, what happens when you have to write about them both? For
example, "both the New York and US Courts of Appeals have ruled ..." Here,
I would prefer to say, "Courts of Appeal" -- but, reasoning that the title
of both courts is "Court of Appeals" I find myself doubting that that would
be correct. And then, whichever we decide is correct, what would be proper
if we wanted to make both courts possessive? "The New York and US Courts of
Appeals' rulings ..." Well, in that case, I suppose it would be better to
say, "the rulings of etc." and avoid the problem that way.
Anyway, I would greatly appreciate an authoritative answer on or off list.