Let me guess- you used pellet hops directly in the boil (no hop strainer of any sort)? Bazooka screen are intended to work with leaf hops, which are widely available, if that's how you want to roll
A good whirlpool will absolutely make a cone of crap at the bottom of your kettle... but it's near useless if you: 1) pump out of kettle to chill or recirculate, 2) don't wait at all after your boil ends to move your wort, or 3) don't whirlpool correctly. To get this cone of crap you speak of, as soon as your boil is complete, get a nice vortex going- for a 5 gallon batch, this can take a good 45-60 seconds of consistent stirring around the outermost part of the kettle. Once it's going real good, let it sit for 5-10 minutes (if you have flameout hop additions, this is when you'll be extracting all that aroma)- you can cover it if you like. Once your whirlpool is complete, gently (read "slowly") rack to your fermenter.