I think a way Luke could end up with his saber without R2 could be like so:

Luke arrives, and Bib takes his lightsaber. Luke talks to Jabba, but instead of just reaching for some random blaster, he reaches out and plucks his saber from Bibs belt (maybe use footage from later in film when Luke grabs it from the Emperor, cropped so you can't see the Emperor's hand) and show reaction shot of Jabba surprised or something and hear saber ignition sound. When Jabba dumps Luke into the Rancor pit, show Lando lowering his mask, for Luke to see, and cut to a shot of him with the saber on his belt. Then later at the Sail Barge, when the craziness begins have Luke jump back up, Lando says something like "Skywalker!" and show Luke with his saber.

Not sure how effective this could be, but I think it works.