On an SP-III 687, I needed to tighten the forend on an aftermarket used Unsingle without altering the wood, to allow switching to the original double or the Monotop. (I've loved the Beretta's ubiquity, and therefore the wide availability of accessories, etc.)
So here's a quick, stable, and free hack: I used a thin silicone film "shim" on the main contact area between the forend wood and the Unsingle barrel. This completely eliminated the slight but perceptible looseness. It also tightened the barrel lockup onto action, eliminating any daylight peeking between barrel and action. Silicone is of course impervious to the heat. For this, I harvested the "shim" from a CPAP nasal mask; - it had a graduated thickness, allowing me to "harvest" the appropriate thickness.
Unrelated to that issue, but another example of silicone's usefulness: In another Beretta thread a readers asked about fixing the action's hinge pin (trunion) which had loosened. It was pointed out to be a simple matter of retightening the pin with allen wrench (from the inside). Hoewever that external hinge pin can be tough to keep from rotating with the wrench. The hack: Lay the action on its side - i.e., with that pin down, pressed onto a silicone bushing. Works wonderfully: the silicone washer/bushing is grabby and is thick enough, and its hole keeps the the convex disk centered. ( Isolateit.com is a great source, or a buddy if you have one at an auto body shop.) (The post also could have noted that the pin is turned counterclockwise to tighten.)