The way I understood it, often you can put a little clip thing inside a normal magazine to not allow more than a certain number of bullets
Yes. Most commonly you see them installed in tube magazines on shotguns to limit them to whatever your state hunting regs deem appropriate (usually 3 rounds). The block can be removed to restore normal capacity if desired.
To use an AR-15 30 round magazine as an example, it wouldn't be particularly difficult to install a kit that blocks the lower part of the magazine, with a shorter spring to install between the block and the follower. It would still look like a 30 round magazine but would only hold the reduced number. The problem would be that this is easily reversed by removing the block and putting the original spring back in place. I can't see the idiots in the NY legislature trusting their subjects *ahem* constituents with such potential evil.