"You know that ol' poly thing that flies around? We move at the pace of the slowest person? I just don't want that pace to be a standstill."
That's true. It's reasonable to expect some progress, even if it's slow.
You will have to see if TJ develops a tolerance for poly. Some people just aren't wired that way. DK will have to make a decision on what to do about that, if TJ absolutely says "no," Then DK will have to choose.
It seems fine to let DK make the call on when you could meet with TJ. Just be willing to offer whatever support you can.