You'll absolutely notice a difference. I wore my pads on ice while they still had the slippery tape that I added to them for an inline hokey tournament. I kept it on there for several games until it was starting to peel off or until the moisture weakened the adhesive to the point it peeled right off. They slid phenomenally well with the tape. On all ice conditions.
I moved the waist straps up on the back plate as well too. I also used to use a carabiner to clip the back plate to the back of my goal pants for the same reasons. keeping the front up and the back down. I have since had a strap and buckle added to the backplate specifically for this reason.
I had the same experience playing at Nassau Coliseum and Madison Square Garden. There are a lot of hot lights shining down on the ice surface. My Coliseum experience was even worse because they even turned off the ice refrigeration. The ice was AWFUL.
I don't tuck my 2200. At least not the front. The back does sit inside the back of my goal shorts. I have suspenders up and over the c/a as well. Waist straps are as tight as I can pull them. Not too tight, not loose.