I do occasionally use an immersion chiller (in fact I will tomorrow), but I skip the pump circulation-induced whirlpool. That’s just more equipment I’d have to set up, clean, and tear down. When I use the immersion chiller, I just drain the kettle through a screen to separate the trub.
FWIW, I just went through the same process the author of this thread indicates regarding the constant clearing of the filter as the wort is being funneled into the PF. It’s a pain, even though I use a hop bag. I must have had to clean it 10 times yesterday. I don’t see much of a way around this at this point other than to concoct a better filtration system as has been described above.
As far as the chilling goes, I still take the lazy approach and it seems to work fine. I use an immersion chiller and ice-bath to drop the temp to 80F in 10 minutes. Then I put the carboy in its fermentation spot - a wine cooler set for 65F - wait 4 hours, remove it, shake it, pitch the yeast, shake it and back into the cooler. As I said, works fine for me. I don’t think there is any drawback in the 4 hours to get the wort from 80 to 65F - once it got to 80 so quickly.
Are you using muslin hop bags? If you still want to go the hop bag route, try the reusable fine mesh nylon hop bags. They work great for me. I use a small individual hops bag for each hop charge when I’m brewing batches around five gallons, or one big bag that I hang in the brew with paper clips clamping it to the side of the kettle when I brew bigger batches.