Create successive Batch script?
I haven't tried to do exactly this before but something tells me it would be tricky. This is from the Batch docs:

The API is primarily designed to integrate nicely with the Form API workflow, but can also be used by non-Form API scripts (like update.php) or even simple page callbacks (which should probably be used sparingly).

I remember trying to set batches outside of a form context before and always resorted back to using a form as I could never get them to work.

You might have more joy than me though so you could try simply doing a batch_set in the finished callback like you suggest. Assuming you're adding some data to the $context variable in your first batch's callback function (such as the node ID) you should be able to pick that context data up again in the finished callback and pass it though to your second batch's setup function.

Hope that makes sense!