Snap caps won't always show the same effect as live fire. Snap caps (usually) have a plastic heavy spring loaded 'primer' or a hard nylon/delrin surface for the pin to hit.
It doesn't really mimic a real primer with it's unforgiving after effect of the firing pin being punched into a metal surface. Then you're trying to pull the shell head accross it opening the gun before the pin is lifted from it.
I'd suspect the cocking linkage has slop in it somewhere,,either one side or both.
Easy way to quickly check for looseness is to UNLOAD the gun...
Then dry fire (no snap cap) one bbl. Then hold the gun horizontal and unlatch the bbls.
Let the bbls open and drop of their own weight which they will till the cocking mechanism engages.
That engagement should be immediate to ensure the firing pin is started to be lifted off the fired shell so it does not drag and cause hard opening.
Many guns will show the bbl's will drop open quite some distance at the breech before that begins.
That opening is the amt you have to drag the fired shell head upwards with the firing pin down hard against it still under mainspring pressure as the cocking linkage has not picked up yet.
The fired shell will usually show a FP drag mark off of the primer cap because of it.
Try both sides separately, you'll get an idea of what's going on.
Some cure the annoying hard opening issue with reloads or certain factory ammo that happens to use harder primer cup matrl. The FP won't bury itself as deeply in the primer and is more easily dragged accross the shell as the gun is opened.
That can work, but it still doesn't fix the mechanical problem in the gun.
I was always in the .045/.055 firing pin protrusion camp.
Don't know where or who taught me that but that's what I've always used.
What ever it is make sure the tip is rounded nicely, no sharp points or chips and remember that even if the protrusion is .060 that doesn't mean the pin will indent the primer .060.
But it could cause problems with a punched primer or the tip hanging up the mechanism when closing the gun depending on the style, ect.
I wouldn't suspect the ejector mechanism as the gun opens easily after 'firing' with the snap caps. It just doesn't when live fired.
Seems either way a problem in there would show no matter how the hammers were dropped.
But it wouldn't be a bad thing to take a look an clean them up.
If you have them off of the forend,,leave them off and try live fire as an extractor gun and see if the hard opening is still there. If it is and probably will be,,then at least you've eliminated the ejectors as a source.
Lots of things to consider.,,Take one at a time or you're just going in circles never knowing what's helping and what may be un-doing your work.
