The Sidesaddle for the Benelli M1 Super 90 can be used on the Beretta 1201FP3; however, the inner radius of the mounting plate's upper and lower tangs has to be recontoured for a flush fit against the Beretta receiver. If this isn't done, the Sidesaddle bows out a 1/4" or so at the front.
As for the mounting of the Sidesaddle squeezing the receiver, there is a simple solution: Don't torque down the mounting screw! Just turn the screw far enough through the mounting plate that the supplied nut will fit over it. Check for uninhibited cycling of the bolt, then use LockTite on the nut to prevent everything from unscrewing.
My Beretta 1201FP3 reliably cycles 1 oz./3 Dram loads with both the magazine tube and Sidesaddle fully loaded.