1. Can Approach grant clearance to go thru intervening class D when
VFR? I am accustomed to this as a matter of routine when IFR but I do
not know about VFR.

I believe so. What they do is "coordinate" with the tower under letters
of agreement that the pilot has no access to. But if they drop the
ball, it's your problem.

However, you may have been above the D when you passed over them (I
don't have the relevant chart). Check for the altitude in square corner
brackets (something like [24]) in the D ring.

2. Why was I given in effect "permission", but no clearance, to enter
class Bravo at 3000, therefore permission to bust class Bravo and
potentially get cited?

You =must= hear the word "cleared" or it doesn't count. It may be that
the controller wasn't aware that exactly 3000 feet was a bust (though
2999 was not). Remember that if you are not under their control (that
is, you are VFR outside the alphabet) ATC can only advise you, not
direct you. When they said "maintain 3000 and you'll be fine" it is
advice and reassurance (which in this case would have been incorrect,
but that's why you're the pilot).

3. Is there a better way for this trip that you can think of? For
instance, is it reasonable to file IFR and then, along the way, spring
a request to circle the area of interest, under the implied clearance
to be in Bravo and Class D afforded by the IFR flight plan?

I don't know if there's a better way. I don't think that one is it
however. Sometimes you just can't do it (due to their traffic concerns).

Jose
--
"Never trust anything that can think for itself, if you can't see where
it keeps its brain." (chapter 10 of book 3 - Harry Potter).
for Email, make the obvious change in the address.