Given that you fly the midfield crossover at pattern
altitude + 500 feet this shouldn't be an issue...

But I don't! We fly the crossover at TPA. That's what
I do, and that's what I've seen dozens of other pilots do.

Otherwise you are descending onto the downwind, which
my instructor says is a no-no. Do everything in or near the
pattern at TPA, says he.

(I missed the earlier part of the thread so this may be dup), but I too do
all my maneuvering at +500 or more above the pattern. Especially if I'm
nordo or get nothing on the unicom. Then I usually like to come in and peak
at the sock, and maybe do a few orbits to look the field over. Or when I'm
coming from opposite side of the pattern. In all cases, when I've finished
looking, I proceed outbound perpendicular to the downwind at +500. And about
a mile from the downwind I will initiate a descending right turn (225deg)
ending at TPA on the 1 mile 45 to the downwind. I've always preferred this
as I get to loiter above the TPA for as long as I need, and then the big
turn onto the 45 becomes a giant clearing turn.

I've seen others inbound from the opposite side, crossing midfield at TPA
and joining the downwind with a left hand turn. That works for them, but I
never liked it because I've seen it bunch up the downwind.

One thing for sure, in the years I've been flying this (entering the
downwind from opposite side) has been the most discussed issue without ever
being resolved.