Missing the point. You aren't trying to warm the cave. The chicks get warmed by making contact with the pad, just like they would with a momma hen. If your setup is too tall or if it's not really adjustable, it won't work.
Don't try to make it too complicated. Just a piece of wire fencing, a heating pad, and something to cover the pad to keep poo off it is really all you need. Adjustments to height are almost a daily thing, and it's really just a slight tweak. The chicks grow quickly and the pad needs to be at...
With only one way in and out, there is a significant risk of a chick getting lost in a corner and overheating. Also not going to be very easy to adjust as the chicks grow.
Missing the point. The way the heating pad works is by chicks coming into direct contact with the heat source. The chicks choose just how much contact with the heat they need, just like they would if raised by a broody hen. This is not an ambient heating method.
Most using heating pads use Sunbeam pads, but any pad without an auto shutoff will work. You do need an adjustable frame to keep the pad up so the chicks can snuggle under. I like to use a piece of of scrap welded wire fencing.
The smaller pad will be fine for that many chicks. I've brooded 12 under the smaller sized pad a few times without issues. The crate may start to get a bit cramped by the time they are four weeks old.