sounds more like your tension spring is not working correctly. That should keep the slack out of your thread as your takeup lever starts to go down to make the next stitch.
The only problem I have with "curly" thread is when it wants to loop around and twist on itself, and then the loop pulls through the tensioner, and once on the other side, I've got way too much slack in the thread and then I'll get a tangle on the underside, and sometimes a thread break.
I'm currently using some thread that is over 30 years old, and don't notice it wanting to "curl" any more than new thread. The cotton I got from Connecting Thread sure likes to curl though, enough that it will pull itself out of the needle when I use the thread cutter. So when I use that, I cut my threads the old fashioned way so I have longer tails.