Pull charging handle back and lock bolt to the rear with bolt catch (even if you have to mortar to get the B/C back), then clear the jams.

Now reach into the action, push the top round down in the mag, uses the charging handle to walk the B/C back forward over the round in the mag you are pushing down, use FA to lock bolt home on empty chamber, then you can shotgun the upper open to deal with the rounds in the mag.

Keep part, is you don't want a live round in the chamber with the bolt locked home as you are screwing with the rifle.

As for fixed mags, about the unsafest thing in the world since when clearing a Jam, you want to drop the mag out first.  
At least with a bullet button, you can drop mag by using a bullet to depress the mag catch, while with the allen bolt type catch wit plug, there is the plug that you would have to remove first, before you could even use the Allen wrench to pull the catch to drop the mag.

The problem with the fixed NY Allen bolt lock, is that you have to shove/install the plug  to make it legal, and to get the plug back out to use the allen key to remove the latch, you pretty much have to drill out the plug.  Think of it as FS blind pinning with permanent cap weld so the pin can not be removed, and if you used something else beside the plastic plug that you could remove without drilling it out to use the wrench at will to remove the lock, then would not be NY legal.

And yes, if you remove the plug so you could get to the allen bolt with wrench, then would have to install (drive in) a new one to make is legal again.

Pretty sure that the Hogue freedom fighter kit is a No-Go for NY, but armaglock would be fine for the NY rig to at least get the upper shotgun open faster itself once the bolt is locked back home.

New York requires a "permanently" fixed magazine unless the weapon is featureless, and magazines cannot hold more than 10 rounds of ammunition.

The state considers any semi-automatic, centerfire rifle to be an “assault” weapon if it has any of the following:

   No fixed magazine
   Pistol grips (beneath action or forward, second handgrip)
   Thumbhole stock
   Adjustable stock
   Grenade launcher or flare launcher
   Threaded barrel
   Flash suppressor
   Bayonet mount
   Magazine that accepts more than 10 rounds
   Muzzle brake or compensator


So with the plastic plug driving in place over the allen bolt on the mag lock once installed, the only way to remove the plug would require drilling the plug out (machining, like that of a FS that its bind pin has been welded over in place).

As for rifle, you end up with something that looks like this,


Or butt stock like this,




Note, even the HK SL-8 is an outlawed weapon in NY, due to do it single stack 10 round removable mag, and its thumb hole stock, although the rifle was imported into the states as a Target rifle from the start during even the federal assault rifles ban.