As far as i know, there is no way of stopping an act ending action once someone talks to the marked NPC. It also happened to me that someone triggered the end of the act 1 while I still wanted to farm with the 5 stacks of the Nephalem Valor. I just had 30 seconds before we moved to act 2 and there was nothing I could do against it.
As you said in the OP, next time that something like that is going to happen, check in your inventory for the less valuable items you are carrying -blue items with low merchant-selling prices or tomes of secrets, for instance- and drop them. Right afterwards, use the space you just got to pick any good items the monster dropped up. If you are fast enough, you could even teleport to town quickly, store 4 or 5 random things in your stash -just right-click on them- to make some space and go back to keep picking things up.
If you are playing with a friend in the game, you could tell him to get the things you drop -since they are visible to all players- while you get the fresh loot -considering he has space in his inventory-.
As a reminder, try to empty your inventory before entering a boss fight. If somebody activated the fighting event already and you forgot, you still have some seconds in which you can accept/decline. In that moment, teleport back to the city, sell some stuff -you don't need to empty everything; usually space for 10 items will suffice- and accept the event. You will be teleported right to the battle with your sanctuary-saving friends =)