You've obviously looked into this a LOT more than I have but a simple idea if minions are a problem-- if some of your allies were to build a banner of command, just standing near your minions and feeding should give enough hp regen etc. to your creeps to keep the wave from pushing, let alone the promote active.
Unless it was the opponents inhib that went down, I didn't watch the video. In that case just switch sides and try the banner.