Please allow us to do The Rarest Specimen and Pizza Precipitation together! [SPOILERS]

I am doing a 100% run for all the new achievements in order and I was planning to do all achievements in one run. This means that I have to do Purple Hat, Pizza Box, and Gas Canister together. Gas canister is fine but is there a way to allow us to do both Pizza and Hat together? I think many people would like to see Purple Hatted G-Man in Pizza Rain. Can’t we just throw each of the props one after the other? This would allow us to teleport all three props wherever we need to use portals. (Including Nihilanth). Thanks.