Thanks for posting the very clear and detailed "how to" videos about the Rem. 870 Synchronizor. Great stuff!
About the Smith & Wesson/ Howa 3000: Yes, you are right.
Smith and Wesson's first Japanese-produced police shotgun was a disaster. That was the Model 916 as I recall. Basically, after that debacle, during the Bangor Punta-era of Smith and Wesson the firm decided that they essentially covered the North American law enforcement market as far as revolvers went, and that they would take on Remington for market share in the police shotgun market. The idea was to offer a sweetheart deal on the shotguns to departments that used S&W revolvers. It didn't really work, as only a handful of departments switched to S&W 3000s from older/earlier models of Ithacas and Remingtons. Of course, Mossberg was also making inroads into the shotgun market. Folks who like the 500 and 590 seem to think the shell elevator on the Remington is a significant detraction. Some people prefer the tang-mounted safeties. Nonetheless, as with anything, there is a sort of "cult following" for the Smith/Howa 3000s among shotgun aficionados. Howa in Nara, Japan built the shotguns, essentially a copy of the well-worn and time proven 870 design with one or two tweaks. The bolt and the slide arms are a bit different to my eye, possibly to keep things running with debris/dirt in the action. Everything is built heck-for-stout that is for sure. I'm not sure what, if anything, is different about the shell elevator.
You can't see it in the photo, but there is a metal badge tacked on at the bottom of the pistol grip with the number of the squad car it was assigned to. I wrote Mr. Jenkins, the historian at Smith and Wesson, before he retired and he sent me the record that it was produced in Japan in 1983 and sold in May along with fourteen others to the PD in Pontiac, Michigan. [I collect all sorts of useless information!

]. It is just a knocked-about 25-years-then-retired police "riot gun" with some coffee and donut stains here and there. Heh. Nothing special: plain wood stock, cheap parkerized finish, 18 1/2-in. cylinder bore, 4-shell magazine for 4+1 capacity. The reason I picked it up and bought it was because all of the controls function exactly like the Remington 870 I've trained on. I try to keep things simple where I can.