Thank you for making my point.

That is exactly why you do not make an adjustment to a reloading machine so that the primer flange sits up off the primer pocket. Which is what you have suggested to the OP. Just because the anvil is already solid against the battery cup you cannot leave the rim of the battery cup proud of the metal head. When you do leave a gap it is exactly the same as not bottoming a centerfire primer in the primer pocket.

If you are 'adjusting' primer seating depth on a shotshell, there is something else wrong.

Flush with the case head. I wrote that several times because the first picture the OP posted showed the primer flange pushed down below flush. Never did I write that the primer had to be left proud of the case head. Wow.

No not WOW. If the flange is below the case head there is a problem with the hull or the primer. No if's and's or but's about it.

Try seating a primer in a shotshell too deep, it cannot be done with normal pressure on the reloader handle.

If you have a MEC Sizemaster or 600 Jr., there is a 1/4" ring that goes under the primer cup assembly for reloading 3" shells. With the machine set for 2 3/4" hulls, put that ring under the primer cup and try to seat the primer too deep using reasonable effort on the handle......you can't push the primer any deeper than what Lyman or other sources recommend.....flush with the metal head.

If you have a MEC progressive, the reason for the stout spring on the reprime tube is so that after the primer is seated to the bottom of the primer pocket you can continue to the bottom of the stroke to charge the hull with shot and powder. If that spring wasn't there the machine would come to a dead stop because you can only seat a primer just so deep in a shotshell. 99.999999999% of the time that means flush with the metal head.

So your suggestion of adjusting the primer seating assembly so that the primer sits up higher in the primer pocket is leaving room for the primer to move deeper, because there is some sort of problem the with primers or hulls that the OP has......and no I have never seen that before.

Some while ago a couple of us started experiencing "light strikes" on FIO 616 primers. To start with it was on my DG101 unsingle and a friends 101 o/u, short while later in became an irritation on a couple BT99's and then later on the bottom barrel of a couple Citori's. All these guns would function normally with any other primer. New pins and hammer springs took care of the BT's and Citori's, 101's same fix helped but did not completely solve the issue. An old lot of FIO I had worked just fine. I observed a difference in the design of the base on Fed, Win and Rem hulls.... not much but the depression for the primer flange is different. I also observed that after installing FIO with my 9000H the center was "flattened" enough to take some of the radius out of it. Made sure adjustment was correct (thanks Curly) and then used a diamond bit to modify the post the primer sets on to create a surface that only presses on the flange.. radius is now back on edges of primer center, and no more FTF after several hundred rounds. Sample size is small but at this point no FTF.
Could go to hell tomorrow but working for now............ Larry

Loaded 50 and tried them today. Zero light strikes! Thanks for the solution and help!

P.S. I did have 2 odd FTF's on the second shot, but not from a light strike. It appeared that the first shot did not cause enough recoil to set the second hammer. These are very light loads so I'm not overly concerned. I might have Zoli USA adjust the sears/springs to a lighter load or just use these for singles. No problems with second shots on factory loads.

Thanks again, garrisonjoe!