In some cases, assets not provided by the beginning of the sprint could cause project backlog items associated with those assets to go back into the backlog
So, you have a problem with a backlog. The sole owner and responsible for the product backlog is a Product Owner. Therefore, you should work on this directly with him. While you can and should contribute to the backlog as well, it is neither your team's nor client's problem per se.
To work with backlog items effectively, you need a "definition of ready". If it is agreed between the team and the PO, then at any moment in time PO can check, are there enough (or not enough) backlog items ready for the next iteration, and take action in advance.
what about when it gets to the point where everything left in the backlog depends on those assets?
If proactive backlog monitoring by PO is being done, and you still have under-populated backlog, then you simply do not have enough scope on that project to fill your capacity.
You have an option of taking another projects on, or helping your PO in preparing the backlog items.
We really want to do scrum "by the book" and have one team on a project at a time so we can really focus on those individual projects.
If you stand by that, you should spend your effort on improving backlog items, assisting the PO (and, by extension, the client). This should keep you busy, especially if you do just enough to keep your next iteration's scope topped up.
Pausing on the project to work on something else would be very disruptive and the team would lose momentum, and waiting around doing nothing until the assets arrive isn't an option.
If you really have many projects with mostly empty backlogs, and you have to switch between them to avoid wasting time, then it looks more like a service, not a project development. In such case you are essentially performing occasional services to one or many customers. Maybe, you should consider other agile approaches, like Kanban, which will be better suited for that (having work-based view, not project-based one).