I unscrewed the cocking piece one turn and now it sticks out far less. Almost not enough. Is there a minimum that a pin has to protrude?
Okay, you have a threaded firing pin which Mauser itself quit using after the 91 Argentine Mauser model. That makes it a bit easier to adjust fp protrusion.
The actual protrusion needed will depend on headspace, your firing pin spring strength, cocking piece wear, the hardness or lack thereof of the primers, and avoidance of risking pierced primers by too great a protrusion. I am leaving out the firing pin weight which also affects this as this is constant. If you do have cocking piece problems, you will generally have problems applying the safety if the Model 20 follows the std. Mauser design. I have such a problem now with a 91 Argentine Mauser rebuild where I had to use an aftermarket replacement firing pin as the original broke. The firing pin and cocking piece go too far forward and as a result, the safety will not apply but the rifle will fire (have tried to fit a variety of sears, triggers, bolt sleeves, safeties for it, and cocking pieces so the problem has been isolated to the replica firing pin length). Solution then is a new firing pin which I prefer to be original this time instead of the gpc replica which had some other issues like firing pin tip softness.
One of the big things that can affect actual ignition is worn chambers allow the brass to move forward (worse with extractor wear) and the cartridge moving forward before firing basically reduces firing pin protrusion. As a result, a lot of folks 'adjust' their firing pin protrusion to get reliable ignition with a worn chamber instead of setting back the barrel and requalifying it. Given the age of the rifle, it is certainly possible that someone did just that especially with the threaded firing pin. I would check the headspace of your rifle first. If the headspace is within the no-go range and the extractor holds the brass tightly to the bolt head, then you can work the math back to determine the needed firing pin protrusion. Some folks have reported that at least .050 firing pin protrusion is a minimum for Mausers in general but a lot depends on whether Savage followed Mauser specifications.
You might try calling Savage as they might have the specs and that would save a lot of grief or posting on a Savage collector's forum and maybe some kind soul has had your problem. Model 20's are pretty rare and some owner might even check their own rifle for protrusion and report back to you.
Otherwise, you might need to do trial and error which can be a drag. To do that safely, you can use primed cartridges with no powder or bullet and set the fp protrusion at the minimum and proceed to lengthen the firing pin protrusion turn by turn until you get reliable ignition. The danger is that you might get a pierced primer that throws hot gas back at you so you will need to wear protective gear to do this.
I have not tried this but seen this described in old timey gunsmith manuals. The other would be using some material in a brass empty case that would deform and hold the firing pin impression--this can give misleading information because you will get some spring back in most materials after initial deformation. Maybe filling the cartridge primer pocket with a soft metal or deactivated primer which you would still need to do safety precautions might do it. But after you did this to get an initial set, you would probably still need to confirm it with live primer test above.
My military rifles, pretty much, have published specifications or other shooters have posted their trial and error results, so that I only have a few old blackpowder cartridge rifles that I worry about finding out the best firing pin protrusion length.
Here is Larry Potter of Midway explaining fp protrusion