I might be mistaken but wouldn’t that suggest that there are two sabers?
We see Luke working on one and cut to R2 and 3PO not waiting for him, so there is no time for Luke to give the saber to R2.
Maybe you could move Vaders arrival at the Death Star or Leia’s failed rescue attempt between the two scenes of Luke working on his saber and the droids walking up to Jabba’s palace.
Well I’m just imagining cutting around a few shots in the middle of the deleted scene, so it would go from Luke working on the saber to R2 emerging from the cave. The handoff still happens, but it’s unclear. I think that’s an interesting way to go about it because the location of the saber is unknown until the sail barge, perhaps as an effort by Luke to avoid violence until absolutely necessary.
This rearrangement also works to tease big elements of Act 1. Jabba’s voice is teased without revealing his corpulence, Luke’s black costume is teased in semi-darkness, and his saber is teased while obscuring its precise nature and location. We also don’t know where Lando and Chewie are, and are only guessing at their part in Leia’s plan. Leia herself is absent for the droids’ arrival at the palace, creating the anticipation of her fate, as well as that of Han.
Finally and perhaps most importantly, the plan is far more clear, since there are two plans. Leia’s plan is unknown, but could presumably have included herself and Lando as bounty hunters taking Chewie in to gain entrance to the palace. When her escape failed, Luke realized that he must use his resources to get them out. He first sends the droids in an attempt to diffuse the situation diplomatically, and when that fails he goes in himself to mind trick or threaten Jabba. Failing this, he realizes that violence is the only answer.