For multi-use or multi-product equipment used to make clinical trial materials, would you expect the analytical methods used to verify removal of the previous API to be fully validated, and would you expect reference standards to be fully characterized?

Because of the nature of the manufacturing process for APIs for clinical trials, cleaning validation per se is not expected. What is expected is cleaning verification. Verification can be done on a single batch where validation involves multiple batches to demonstrate consistency. Visual inspection is often suitable.
Reference standards (particularly impurities) of API used in early clinical studies may not be fully characterized depending on how fully developed your process is. Full characterization is expected later in development, once the process is more fully understood.