Weird behavior pasting into multi column component

We have a custom component that allows multiple columns to be displayed, and each column has an embedded parsys.  We're seeing strange behavior pasting into that parsys though.  

If we copy a component in the left hand column:

We don't get a paste option when clicking on the right hand column.

But if we select the main parsys for the page, we get a paste option there:

And now if we click on the right hand column again, the paste option is suddenly available and we can paste successfully:

Any way to address this?