May I suggest the following application:
Magellan explorer (link to the feature page, see section
Background operations).
It is not cheap with a price of 39.95 USD, but it fits your bill perfectly. Actually, it is capable to put multiple file operations in multiple locations in a queue! A 30-day trial is available.
No affiliation, just a happy paying customer. This piece of software was the first one I bought through the internet, just because of this feature (and you want it you can pry it from my cold dead hands!)