Seems like there are only two things that can be the problem here.
1. the pin is not rebounding as it should (of course...)
2. the hammer is not sufficiently lifted from the rear of the firing pin due to wear of the cocking block

When you begin the downward movement of the side lever, you should have a distinct feeling of resistance before the block begins to drop.
This is the cocking block pushing the hammer away from the rear of the firing pin which allows it to retract from the primer well before the block begins its descent.
You know you are pivoting the hammer because there is a springy feel to the lever - push it a little and it comes right back up from the pressure of the main spring.

My thought is that if you have this resistance, then the cocking block is probably doing its job and the problem lies in the firing pin.
If your side lever begins its drop with little or no initial resistance, then your hammer is not being lifted early enough.

There are excellent drawings of the whole action in Winfer's volume #4 on the W.R. rifles.