If I were the OP, I'd get a room for the prior night at a hotel where I could get a guaranteed late check-out (i.e., an SPG property) so I could shower and have a place for my luggage, etc. I might also consider getting a day driver on top of that, because a negotiated day rate to take you from EZE to the centro, from the centro to AEP, and also on a sightseeing tour might be similar (and more comfortable) than dealing with your own transport for each sector.

The passengers near you on the AEP to wherever segment will have appreciated your shower.