How do I specify an image reference in a Drupal 8 REST POST request body?
I tried again with just the image ID, and it worked perfectly. Thanks
  very much!


To elaborate...

After the image file has been created in Drupal, and you have the File ID you'll be ready to create/update Nodes. Instead of setting the src value on the image field you just need to set the target_id value.

Change this:

"field_product_image": [{"src":"/sites/default/files/2017-03/samplelogo_1.jpeg"}],


To something like this:

"field_product_image": [{"target_id": 123}],


If you're using JavaScript this would typically be accomplished with 2 async calls. The first call would POST the binary file data to Drupal (or base 64 encoded string) to obtain the File ID, the second call (which takes places in the "success" callback of the first call) would then be used to create/update the node's image field with the new File ID.

The following d.o issue is an important one to follow and is very much related to the Question: https://www.drupal.org/node/1927648