DBU isn't very oxygen sensitive in my hands, I never took steps to store it away from air. It will probably absorb water to some extent. I dried mine over sieves for a few days.
EDC is rather hydrolytically unstable, not very oxygen sensitive.
I think the N2 in the case of these reactions is more to create a dry system with positive pressure to keep water out of the reaction, not oxygen.
I would definitely suggest against trying to do this as "one pot' The amount of garbage you will end up with is likely very high, and unless you plan quite carefully, there can be a multitude of sideproducts, some of which may prevent you from forming any product at all.
Organic chemistry is hard enough with pure materials, take the extra time to purify, and you usually increase your odds of success by doing things under water and oxygen free conditions. You should use dry solvents for these reactions (especially the EDC coupling).
Caveat: Some reactions need a bit of oxygen or water to work, but these are exceptions, and neither reaction you describe seems likely to need such catalysts.