Hello, Fallon Kid:
Here are some things to think about, please:
Win LARGE rifle primers have been easy to ignite on the first strike.
Some Armisport Spencers did not have a self retracting firing pin, otherwise called an "inertia" pin.
The inertia one with a coil spring flies forward on striker impact, hits the primer and then the coil spring pushes the pin tip into the block so the tip does not remain against the primer and possibly break if the block lowered before the hammer retracted.
You should be able to remove the block assembly by removing the lever screw and holding the block assembly as it drops from the receiver.
With the block assembly removed, test for pin retraction by pushing on the sliding striker in the upper block to see if the pin moves freely forward and upon releasing pressure on the striker, that the pin self-retracts below the block face.
If the pin moves forward and rearward it should be ok.
It is possible the shaft of the firing pin or coil spring are damaged.
Another remote possibility is that the mainspring is not imparting sufficient force.
One more possibility is that the large rifle primers are large PISTOL primers. Both have the same cup diameter, but the large pistol cup is .003" less high, which can put the cup face .003" deeper in the case pocket. If sure the primers are large rifle, the cup face should rest .003" below the case face. If seated insufficiently, just flush not .003" below, that may allow the primer to seat itself .003" during firing pin impact, but then the blow is cushioned as the cup moves forward.
Please let us know what you find.
All the best.
El Supremo/Kevin Tinny