I’ve done Poly the last two 7/4’s. We all have our personal definitions of insanely crowded, but I would not call Poly insanely crowded on 7/4. Yes, the resort overall is very busy. The reserved beach area is wonderful for Poly guests. You realize just how many non-Poly guests are around milling outside the fence while you get let through.
They have a DJ and characters on the beach - it’s tons of fun. Your 16 month old will be a little young for the dance party, but maybe it’ll provide some entertainment value? Last year, Goofy and Donald were there.
I have seen people bring towels/blankets and start setting up spots towards the side of the beach where the castle is visible (towards the fire pit). Just when people start popping a squat can be variable, but given the restricted access you don’t need to stress too much about it.
I’ll caveat that exact procedures, entertainment, and setup can change year to year, so just be observant.
FWIW, some info from 2018:
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This pic is actually 12/31, but the same setup applies for 7/4. Metal barricades restrict access to this beach area. In my experience, enforcement is quite strict.
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Boom! (Taken from a TPV room, not the beach, but the beach has the same general angle).
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Hope that helps! With apologies for the hyperbole, I absolutely love Poly on special days like 7/4 and 12/31 - it’s a great location and there’s a fun vibe that’s hard to explain.
Happy to answer any questions.