How do I set the value of a custom entries order field from a plugin?
I was close. I was correct in assuming my syntax was incorrect for setting the value of an entries field.

Since an entries field is an array of elements, not just a single element, I just needed to set the value of the field as an array instead of a string.

Changing 

$cart-&gt;setContentFromPost(['entriesFieldHandle' =&gt; $entry-&gt;id]);


to

$cart-&gt;setContentFromPost(['entriesFieldHandle' =&gt; [$entry-&gt;id]]);


seemed to do the trick.

To zoom in a little more, the value needs to be set with 'entriesFieldHandle' =&gt; [$entry-&gt;id] instead of 'entriesFieldHandle' =&gt; $entry-&gt;id.