FWIW, I do a modified ‘no-chill’ by using my immersion chiller to get the wort down to 120* or so, usually in about 5-10 minutes, then chill the rest of the way in my ferment fridge, and I haven’t had noticeable issues with clarity.
To Cellars’ points though, the other practices mentioned will help with proteins that cause haze. Some swear by a protein rest in their mash, but I’m not a fan as it can wreck head retention if not done perfectly.
Are you rehydrating your Irish Moss before dropping it in? Most instruction kits that come with it don’t instruct the user to do it, but I have heard it makes a big difference. Basically just take about a cup of wort at the beginning of the boil, put it into a coffee cup with your Irish moss, and add the whole thing @ 15 minutes. Whirfloc is pre-rehydrated IM.
Cold crashing will really help precipitate out particulate. Depending on where you live these days, just throw your fermenter in the garage for a day or two and it will drop out the yeast/particulate into a dense cake at the bottom.
Finally, if you want to use gelatin, IMO and IME its a cheap easy way to get to another level of clarity. There is a thread somewhere on NB debunking a lot of the methods for using it found on the internet. Essentially, the RIGHT way to use gelatin (according to this guy’s master-baker grandmother…who I implicitly trust):
-sanitize a cup/measuring cup
-add a cup of cool water (60-70*)
-add 2-3 T of store bought plain gelatin
-let it sit there for 15-20 minutes to ‘bloom’
-put it in the microwave for 30-45 seconds
-add to COLD beer in fermenter (no need to stir, it will diffuse)
-wait minimum of 2-3 days