How have you been joining up until now? Don't you just run the needle through the picot? Isn't that one of the basic ways to do it in needle tatting?
You get to the spot where the join should occur and run the needle through the picot you are joining to. You may have to pull the thread through if it is awkward, but then you just continue with the ring you are making. I have always envied needle tatters for this.
If I confused you before, please forgive me, I just didn't notice this was from the needle tatting forum.