Bulk Collection Manipulation through a REST (RESTful) API
Solution 1:
You might want to think of the change task as a resource in itself. So you're really PUT-ing a single object, which is a Bulk Data Update object. Maybe it's got a name, owner, and big blob of CSV, XML, etc. that needs to be parsed and executed. In the case of CSV you might want to also identify what type of objects are represented in the CSV data.
List jobs, add a job, view the status of a job, update a job (probably in order to start/stop it), delete a job (stopping it if it's running) etc. Those operations map easily onto a REST API design.
Once you have this in place, you can easily add different data types that your bulk data updater can handle, maybe even mixed together in the same task. There's no need to have this same API duplicated all over your app for each type of thing you want to import, in other words.
This also lends itself very easily to a background-task implementation. In that case you probably want to add fields to the individual task objects that allow the API client to specify how they want to be notified (a URL they want you to GET when it's done, or send them an e-mail, etc.).
Solution 2:
Yes, PUT creates/overwrites, but does not partially update.
If you need partial update semantics, use PATCH. See http://greenbytes.de/tech/webdav/draft-dusseault-http-patch-14.html.
Solution 3:
You should use AtomPub. It is specifically designed for managing collections via HTTP. There might even be an implementation for your language of choice.
Solution 4:
For the POSTs, at least, it seems like you should be able to POST to a list URL and have the body of the request contain a list of new resources instead of a single new resource.
Solution 5:
As far as I understand it, REST means REpresentational State Transfer, so you should transfer the state from client to server.
If that means too much data going back and forth, perhaps you need to change your representation. A collectionChange structure would work, with a series of deletions (by id) and additions (with embedded full xml Representations), POSTed to a handling interface URL. The interface implementation can choose its own method for deletions and additions server-side.
The purest version would probably be to define the items by URL, and the collection contain a series of URLs. The new collection can be PUT after changes by the client, followed by a series of PUTs of the items being added, and perhaps a series of deletions if you want to actually remove the items from the server rather than just remove them from that list.