We enjoyed the quiet time on the beach during our first/referral visit. Are the chairs under the palm tress open to all guests?? We had the black bands first visit, this April we will have the white.
Beach is sectioned off as Premier...to the left when looking out at water...which may have been the palm trees you mention. I believe, just like the deck, that Tower now also has a section. And than, there is the open section further down to the right. Not sure there are many, if any trees.
Had white band in June and had no problem with sun beds under palms, Premier extra seem to be along the back, including the "four poster" type beds. You should be fine....
We had white bands in april and no one said anything to us. There was also no demand for beach loungers. There was maybe one other couple out there with us.