First, welcome top the forum.
I have not seen the jacktight tool before. That looks very good so thanks for that.
IF your jack has the small hole as pictured in the first photo on the jacktight page you can slide a small rod (I use a small allen wrench) thru and get the wrench in between the jack and the body of the guitar. A less elegant option is to grab the very end of the threaded piece of the jack with a vise grip and again slide the wrench between the vise grip and the body of the guitar. You will likely mess up the threads, but that may not be an issue. I would also suggest a dab of lock tite on the thread to keep things in place once you get it tightened up.