I would recirc hot wort out of the kettle through the hopback and back to the kettle. Creating the whirlpool as the wort reenters the kettle. Yes you may loose a little hop aroma volatiles when it goes back to the hot kettle, but I'd say use more hops and/or a bigger hop back.
You will pick up some debris from the hopback actually, so adding that to the whirlpool may help keep it out of your plate chiller.
The other overall option is to stop whirlpooling and use a mechanical means to keep break out of the chiller. Like a hopstopper.
Actually use the hopbacks filtering capacity to help you out and build a hopback with a large screen for the break in there instead of in the kettle. So then you'd kill the heat, run into the hopback and into the plate chiller and done. So it would be a grant device that could also hold hops. That would save a little time too.