I have tried to use the CJ 39/44/50 list in tournaments at several times, but I have only been allowed once. I see no need to change it, if that would lessen your chances of getting to play. If they want to play straight CJ 39, go with that even!
The one I got to play was 1500, and had Great Harlequin, 3 DeathJesters, Solitaire, 2x6 Troupers, Jetbikes and Venom I think. It did badly, but it was fun to play, and most opponent were amazed at the way the Harlequins worked. They got shot to crud, of course, and with no save in hth they weren't overwhelming. But I did crack some serious targets with the list, and had fun. The look of stunned fascination on the face of the Marine player who got his Chaplain and four DeathCompany-marines handed to him on turn one facing a single Great Harlequin was priceless!