Perhaps you will know Carcano. Used Einsteckläufe do appear on Egun and similar. But I assume that only a gunsmith would install most of them. They are specific not only to the shotgun gauge but also the barrel length. Perhaps some can be shortened to the new muzzle length and the adjusting screws and their housing shifted backwards also. But also they would need to fit the new choke or at least be adjustable somehow to make a firm fit to the muzzle/choke of the new gun. I can see that, at the breech/chamber end some of them, (such as S&K), are adjustable to take up any space there at the leade of the chamber.

I have one of the older Krieghoff style Einsteckläufe that is well short of muzzle-length, in .22-Magnum. In fact, it fits into a recess in the stock along with spare cartridges. At 70m it is quite adequate for small game such as hares, but it would be handy to have a muzzle-length Einsteckläufe in 6x70R or similar with not so much back-thrust on the breech end of a Drilling.

Just to mention here also, that I have 3x very short Einsteckläufen, little more than the length of a cartridge in .22LR, .22 Magnum and .22 Hornet. These 3 all fit in my 5,6x57 RWS. My young son was able to learn to shoot with the .22LR, then the .22 Mag. Next the 22 Hornet and finally he shot a fallow deer buck, his first with the 5,6x57. As a way to introduce young children this system has much merit. In New Zealand there are no minimum calibre regulations and the strongly constructed 74 grain RWS-Kegel Spitze was more than adequate.