Just a thought but could the rebounding firing pin found in the Hepburn action combined with the use of large pistol primer have contributed to the primers backing out? I've had Rem 9 1/2 LR primers back out slightly in a .38/55 Hepburn with a moderate smokeless load of SR 4759 but when the same load & bullet is used in a Highwall, the primers don't protrude at all. Cases extracted easily in both rifles.
Spud

The plot thickens............................

It's quite typical to leave .010 to .012 for Hunting rifles so there is enough room for dust, dirt and other debris so the breech block will still close. 

JLouis

there are 2 things to consider when headspacing a falling block.
first is the gap between the back of the barrel and the block.
0.005 clearance should allow room for any reasonable fouling, variation in rim thickness, etc.
should rim thickness variation exceed tis, then attention to the front side of the thicker rims is required.
second is the depth of cut of the rim recess in the barrel.
should that place the rear of the case level with the rear of the barre, there will be 0.005 headspace, probably max ideally.
the fact that the block operates at right angles to the axis of bore is probably a plus, as it will tend to wipe grot away.
what is consisered max acceptable headspace?
the rifle in question could well exceed max headspace, taking into account what could go wrong even at black powder pressures.
if the back of the case is level with the back of the barrel, then the chamber is ok, and either the barrel needs to be set back, or a thicker block will solve the problem.
if the rim recess is too deep as well, the the barrel needs to be face off, and then set back to suit.
the problem here is that the sights will then most likely not be top dead centre, so a rechambering will also be necessary as the barrel will need to be set back 1 full turn.
the issues presented by the o.p.will then go away.
low enough pressures will allow the case to slide back in the chamber during firing and after the primer has backed out.
while this might have normal looking primers. the primers can flatten or wrap around the firing pin, gripping it.
higher pressures as with duplex will give enough pressure for the case to grip the chamber walls sufficiently to allow backed out primers.
probably the latter situation is better for accuracy, as the case is not moving as the bullet is leaving it, the gap between the case mouth and the chamber transition is not as variable, and is not excessive, and there is less chance of case seperation in the web area.
if the chamber is an original, it would be a mistake to rechamber with a 45 degree transition reamer so common today for so many reasons.
keep safe,
bruce.

craig,
the case headspaces off the rim.
holding it back onto the block with a bullet simply induces headspace, and you then need longer brass to avoid a gap between the case mouth and the chamber transition.
with black powder and cast bullets, some of the bullet will bump up into there, or be forced into there other ways - a negative for accuracy, as well as a possible cause of leading.
putting in zigs does not necessarily cure zags.
plus there is the safety factor.
keep safe,
bruce.

craig,
thinking can only be a good thing.
if the cases were bottleneck, you could headspace off the shoulder.
the problem here is that you are relying on the web more than usual to hold the pressure, and while it is probably ok, you are stretching a friendship.
you might do ok with short brass in an old chamber, as the transition angles in them were lower than the modern 45 degrees, so unsuited to cast bullets.
the bumped up bullet can slide more easily over a lower angled transition.
keep safe,
bruce.

Possible annealing could help?
beltfed/arnie