I'm gonna suggest that before you remove any type of trap that you first try removing the Tub Screen in the tub first, and make an attempt at this point to clean out your pipes. (It's the 'fixture' that transitions your tub with your piping. It has the cross-hairs on it.)
I'm not a plumber so I'm claiming some ignorance of plumbing and such, ... The tub screen inside the tub requires a special tool that you can buy to remove the screen. Coincidentally, it's called a Tub Drain Wrench. Any Home Center or Plumbing Supply house has one. I removed the screen in my wife's bathroom and it came off pretty easily. I don't think it's ever been removed in the 25 years the tub has been there. I was able to clean the pipe out pretty well after it was removed. I then cleaned up the screen, both the threads and the female piping in the tub, and put some Plumber's Putty down before I screwed it back down. (I even put on some Teflon Tape.) It shouldn't be torqued down too much. Snug, yet not loose. The plumbers putty will do the rest. If there's any excess that's squeezed out, just run a toothpick around the perimeter and throw away the excess.
My best to ya and hope this helps. Personally, as John 2000 says, if it's what you're doing isn't working, get a pro or take a stab at my alternative.