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.