IAI tried something similar several years back. It was basically a 'Baby' Remington 870 in .357 and .44 Mag. called the "Timberwolf'.
Personally, I LOVE mine but it fizzled in the mass market. At the time of its conception, most LEO holsters carried some variation on the 4" .357 theme. One of the major marketing targets for it (IMO) was the LEA market as a patrol carbine with ammo compatability with the issue sidearm.
As a concept this has a lot going for it on several levels, from a practical perspective.
Howerver, there were a few design issues brought on mostly by trying to cover too many bases at once that tubed it, IMO.
1: You have to top off the magazine with the action open. No biggie for most civilians, but a major concern to an LEO.
2: The receiver was made with a big. clunky optics mount integral to it. While it is arguably hell-for-tough, it looks sort of weird and precludes the mounting of any standard receiver sight on it. It may have been added for the 'sporting purposes' points toward import, or from the mistaken assumption that most users would want a 'scope or Red Dot on it. Whichever it might of been it screwed up the aesthetics of an otherwise trim and handy little carbine. It doesn't really get in the way for carrying at the balance point, but from a purely functional standpoint it could've been done just as well with a separate conventional mount if it just had to be done.
3: The suggested retail price was outrageous compared to competing lever or semi-auto designs. You could buy a Marlin 94 for $100 less, retail-for-retail, almost anywhere. This changed quite a bit after it became apparent that most LEAs were switching to semi-autos and that their primary target market segment was thereby kaput. I bought mine NIB off the wall at Bradi's for $239. It had been marked down from a still-under SRP $399.
Those niggling bits aside, it is a truly great little all-around woods walker for small game and plinking. Extremely accurate, slick working, fast handling, lightweight..the whole nine yards. As a HD weapon, especially in a more urban setting, it'd be hard to beat for those whose budgets or physique couldn't handle a 12 or 20 ga. shotgun.
I personally like the concept you have, but it's probabvly more-than-evident that my tastes run contrary to the bulk of the market. I grew up with pumps and find them easier and faster for me to make accurate repeat shots with than any other manual action type.
FWIW, a couple of suggestions should you decide to pursue the concept.
Take a close look at the way the butt stock adjusts on a Timberwolf. It's not complex and is somewhat limited, but with some fiddling you can make it as easy and natural to point accurately as a custom shotgun. The sights become almost superfluous: you look at the target with both eyes open (just like a shotgun) and the can dances or the bunny drops.
Make the safety ambidextrous, on the tang let's say.
Make the magazine so that 'tactical' reloads or topping it off can be done with the action in-battery.
MARKETING!!! Have a campaign to show where the advantages are for the consumer. Show them where and how a pump shades a lever gun and why having a carbine in a revolver caliber is so practical and multifunctional.
Try to keep the price competitive. Tough to do, as Marlin, Winchester, Taurus/Rossi have long ago amortized their R&D, tooling. etc., have huge capital support and have the name rec and distribution edge. You're gonna need to make full use of modern manufacturing technology, materials and design to do it. Even then, you're gonna have to convince the consumer that it's the better choice somehow.
Done right and sold right, I think it can be done. If I could tell you just how exactly to do it though, I wouldn't still be working for wages.
Good luck, whatever you decide.
