My understanding is that with modern components the height of the brass doesn't always mean what it did decades ago when shell hulls were made mainly of paper. Or, you can have a plastic shell with low brass that is just as powerful or "hot" as a shell with higher brass around the base. But generally speaking higher brass does mean a more powerful load. Saigas are designed along military use lines which means they like powerful, high power shells out of the box. They weren't designed for shooting quail.
I'm not sure why it was recommended that you buy a drum magazine as a remedy for this problem. If anything all the drums I know of for Saigas, ProMag and MD Arms won't allow 3" shells or roll crimped European shells like Rio. A stick mag will allow you to shoot pretty much any shell you want up to 3".
There are many of these shotguns that will run anything from Winchester Universal (and the like) to high power buckshot and slugs and everything in between. And often I've seen where an S-12 was finicky in the beginning but as it got broken in it ran much better with fewer FTEs, stovepipes etc. First I would check the gas ports, it's easy to do and doesn't take a lot of time. Because if there's a problem with the ports, nothing else you can do will correct it. I can't find my factory plug with two settings like yours so I can't see how big the #2 setting hole is to compare it with the #6 setting on the DPH plug to tell if it allows as much gas to pass (go ahead, laugh).
Again, the physical height of the brass will not always tell you how powerful the load is but generally speaking more powerful loads do higher brass. But there is no other physical consideration that would make one or the other run better or worse. It's what is inside the shell that matters, not the height of the brass....if that makes any sense.
You can't go wrong IMO getting an autoplug but again, if there are other problems it will not magically correct them. Oh and you might wonder, if there is a plug setting that allow a lower gas producing shell like Wally World birdshot to cycle then why not just set it for that knowing any shell that produces more gas should run ok too right? This would mean that the carrier would slam back violently (or more violently) than is necessary to eject the shell and could damage the trunnion in the rear of the receiver. The point is to have close to the same amount of gas cycling the gun as possible no matter which shell you're shooting. This is the beauty of the autoplug.
I've done a lot of talking here but let me say this, I'm no expert with this stuff. I just know what I've learned since I've been messing with Saigas and reading mainly on the Saiga-12.com board. So if I'm off on any of this whoever knows better please comment. I'm always willing to learn.
Here's a vid showing how the autoplug works and is adjusted;
http://youtu.be/7DIeY5Q2pjs Turn the volume down