Since you're using a plate chiller, I assume you've got a pump. If not, the following will likely be irrelevant:
I just recently started doing a whirlpool knock-down recirculation where I pump the wort through the chiller (I've got a counterflow, but same concept with a plate chiller) at the end of the boil, and put it back into the boil kettle through a whirlpool inlet. I've notice a couple of advantages:
1. You get the whirlpool effect on dropping out the trub/hop particles so not as much makes their way into the conical
2. You bring the temp of the wort in the kettle down so as to limit continual isomerization of late hop additions and retain better hop flavor and aroma
You might try giving that a go and see if you get less trub/hop particles in the conical -- it's been my experience that it helps quite a bit. Cheers!