You need to to sprints, intervals and tempos on your solo rides. In fact you need to make your solo rides so intense, the group rides will appear simple in comparison. You need to hit max-HR 5-10x per solo ride. Along with getting dizzy and throwing up. After a couple weeks of this training, the group rides will be a piece of cake.

Also try drafting on the downhills. Latch onto someone 5-10 seconds before the top of the hill and follow them all the way down. You'll have to be hitting the brakes to avoid rear-ending them. Your HR will recover by the time you hit bottom of hill.