Years ago my brother bought a used Remington model 11, and after firing some slugs, it developed a problem that appears to be trigger related.

We tried to tear it down, however the trigger plate screw (screw at near of receiver, holds trigger plate in) appears to be seized up.  If have read this is a common thing on older Model 11's and A5's.

Is there a way to unseize the screw, or drill it out safely?  If I send it out to a gunsmith, my concern is the cost of shipping plus the gunsmith fee could be steep on a shotgun that is worth around $400.  Sending it out could cost $100 in shipping alone.  The local gunsmiths I asked would not do it themselves.

In other words, is removing the seized screw something a person with basic tool working skills could do, or should it be left to a professional?

Had an old A5 had same screw problem. First, make sure your screw driver exactly fits. You can pick up a small butane torch and try heat. Try penetrating oil. If you have a drill press, get a vice to hold reciever. Use the drill to hold your bit. Useing the vice and drill press, you might break it loose with the chuck but a wrench can be used for more torque. Alligned in drill press the bit is not likely to slip out.  Good Luck.

Heat it and let it cool a few cycles. That's where I'd start.

I have a heat gun.  Would that put enough heat out?

Personally I'd use a hand held propane torch if possible. You may need to fab up a makeshift "shield" out of some sheet metal to protect the immediate area surrounding the screw to prevent flame damage.

I'm not sure a heat gun would get hot enough or concentrate heat as precisely as you will want.

Multiple cycles of heat and a 50/50 mix of ATF and acetone as penetrating oil. Screwdriver in drill press as described above (or a screw jack, if you can find or make one). Expect to do this more than a few times before it breaks loose.

The max temp is 1000 degrees F.  The gun came with clip on nozzles to direct and focus the heat area.

I'm going to attempt the cycle of heat and penetrating oil.

@Moondog , well, did it work?

I'm dealing with a similar issue trying to remove two screws from this:

I haven't had much progress.  I tried penetrating oil and applying heat, but haven't tried a drill press or arbor press on the seized screws.

I'm assuming you're dealing with the larger aft screw. The threads on the opposite side of the receiver are where I'd be focusing my attention (heat and penetrating oil). I've been pretty lucky in that I haven't had any trouble with those but it sounds pretty common. I see them buggered up a lot.

Since the finish is gone, I would soak this one in Evaporust.

We did. That's the "after" pic above.  

It's one of several belonging to an elderly friend of a friend. I was tasked with cleaning them up for preservation or disposition. The recently-deceased wife didn't want guns in the house so the man stored them in an unsecured camper trailer.

I'd like to chop the barrel, install a choke, parkerize it, and make a beater turkey gun if we can get it running again.

Sad.