This used to drive me crazy. I tried all the suggested options. Then I read in Kunze, Technology, Brewing and Malting, 2010 ed. p. 371: “Many breweries mill the hops very finely immediately before adding them, and then precipitate the finely milled particles in a whirlpool.”
Mitch Steele at Stone, said that some pros mill their leaf and even pellet hops before putting them in the boil kettle as well (CBC 2010, Dry Hop Seminar). An additional benefit is increased utilization, especially with leaf/cone hops.
I grow hops and grind the cones before using. Pellets go in straight. No bag, strainer, hop catcher, false bottom, braid, etc. Just a ball valve at the bottom of the kettle with a 90 degree elbow on the inside.
I now mill all leaf hops (in a coffee grinder) and after doing a whirlpool and rest, the hot break mix stays in the middle enough to allow me to drain out through the bottom ball valve without any problems (drain very slowly to keep the trub mass in the center of the kettle). Once it starts to pickup the trub, shut the valve. Virtually no hot wort transfer and no need for any type of strainer at all.
Good luck.
P.S. I have a lot of that stuff (bag, strainer, hop catcher, false bottom, braid, etc.) in a box now. ;-)