I would start with a single tablespoon of graphite. A little graphite goes a long way in my experience. You can always add some more.

I don't know anything about a Pacific 266 but if the shot drop tube has a "bottleneck" at its bottom end, you might try enlarging the hole in its center with a small round file or a drill bit. That worked wonders with my 28 gauge MEC 9000 and the increase in diameter was only about 25 thou.

That usually solves the problem Frank. I advised polishing the mouth of the tube with emory cloth as there is quite often a roughness, for a better term, of the chrome plating.

Sound advise Jeff! Really said "a couple" as a general description, actually planning to start with a conservative amount in a small quantity if shot. Having had a bit of experience with graphite in industrial settings you are correct, "a little may be a lot"!
As to enlarging the tube this one is straight, no bottleneck, no way to enlarge, and I have polished the +%@* outta it! Mirror finish.

I have no doubt that graphite could help. My issue with graphite is it's a lot like using Prussian blue, if you aren't careful with that stuff, it can & will get everywhere with a half-life of U-235. I just don't want to run graphite through my loading press if I can avoid it.

As Paul suggested, raise the shot drop tube up slightly so it isn't touching the bottom of the wad when the shot drops if possible. Use the best quality of Magnum shot you can find, and add a small amount of graphite. It is a pain when it bridges!

Drop tube up or down, makes no detectable difference. I'm convince it's just a function of shot size vs ID of the tube. Gonna start the graphite treatment experiment tomorrow at the shop. If a mess ends up on the floor there Ho-hum, definitely don't need a graphite mess on the light color tile floor in my gun room! This is really a tiny bore gun and I knew I was in for some suffering after reading of others issues and trials but wanted a .410 SxS just 'cause I did. Not sure whether it's to be late season doves or the first quail hunt but I WILL have the gun in the field soon WITH my shells in it.

As Churchill said, "Never, ever, give up."

Persistent as rust!

I've tried powdered chalk, no joy.
What I have found is powdered graphite as others have said but I put shot into my RCBS tumbler with the graphite and let it do the work.
I only use magnum shot, I don't experience barrel leading.
I've been trying to use up some oxidized shot and I soak that in white vinegar then tumble that in graphite. Still not perfect but it helps.
Also I use a single stage MEC 700 I converted for 410. After I seat the wad I lift up the handle some before dropping the shot, I keep a dowel handy to rap on the drop tube.