We have a team that works in Scrum and a PO who prioritizes the backlog. Outside of this, we have 3 project managers that hold the communication with our clients (each one with 2-3 different countries). They (instead of the PO) are the communication point with the clients. Also we have a chief PM, who holds the overall roadmap of all the projects. The team estimates and does a little bit of each project's work in each sprint, depending on then deadlines and priorities.
However more often than not, a client will put through some last minute changes, that are not small, and he wants them delivered in 2 days, therefore blowing up the rest of the sprint. This leads us to trying to juggle too many things and compromising in quality at the end.
We tried to bring the clients closer to us to let them understand how we work, but their nature of business is advertising and media, and therefore their response usually is "the ad goes live in 2 days". Therefore their product has to be ready in 2 days.
I know this setup is far from ideal, however how do you tackle the "client" part with the last minute changes, given that it's only one scrum team that has to cater for everyone? Or, even better, how do you prove that this is inefficient?