The concern right now, is that from the time the set screw makes contact, until the sear will not engage reliably and hold the hammer, is probably no more than 1/2 turn.

So dellet, when you turn the screw in what is tripping the hammer?  That sound like a crazy question but it’s not.  The front trigger is what the screw turns against, so if it is close to the sear, turning in the screw could trip the sear and hammer before tripping the rear trigger.  If the rear trigger is tripping (then tripping the sear and hammer) when the screw is turned in, then the trigger may have wear where the rear trigger pulls down under the front trigger when setting, which would cause a short release distance.  This is hard to explain so hope it makes sense to you.  I do have questions about the hammer full notch and sear nose condition also, but don’t think they are your problem here.
Bob

Click on the below link and then go to post number 15. Its a drawing and parts list for the 0441/2 the 441/2 and a few others. Part #62 is the sear and it is quite different than Chuckster's PDF drawing and the triggers and how they operate are also not the same. The double set trigger parts start at #53 and go to #67 and are on the lower right hand side.

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More pictures that may help.
Bob

This is a picture of the right side of the front trigger.  At the top of the slot above the pin hole is the working part of the trigger.  To the front is where the spring pushes keeping the trigger forward.  To the rear, the small triangle area, is where the rear trigger hooks when the trigger is set.  This is the area I was referring to in my post above about possible wear, along with the nose of the rear trigger. The screw pushes against the bottom of the rear extension to adjust the the set trigger and the top of the extension is what pushes the sear when shooting without setting the rear trigger.

As are yours! It is sometimes difficult to try to explain to someone what can actually be easily done on their own. If they can watch someone do it but one time they will have it for a lifetime and they could then help somebody else out.

Bit of an update, appears to be operator error of sorts.

To clarify, this is a CPA trigger set in an original 44 1/2.

I pulled an original trigger assembly from another fire for comparison and they are a bit different, mostly pin size, springs are interchangeable. 

Sat down with the DeHaas book and the trigger assemblies and went through adjustments on the table where I could see and feel what was going on.

I’m still not 100% sure what is happening, I think the fit of the CPA trigger assembly into the original action isn’t too tight, causing a bind.

By the book adjustment is back off the screw, set the rear trigger, adjust the screw (which basically just engages the front trigger) until the trigger trips the sear. Back off 1/4 turn and check function.

Installed the trigger assembly and the hammer wouldn’t not set.

Went through the adjustment procedure again. Hammer set and functioned correctly.

Pulled the trigger assembly and re installed. Hammer failed to set. 

Backed off 3 turns, repeated adjustment. Tripped the sear at 2.5 turns in. So after removing and re installing the trigger assembly, set screw adjustment needed to be backed off 3/4.

Pulled the assembly a couple more times, each time the same thing. Adjustment screw needed to be backed off and reset before the hammer could be set.

Main hammer spring tension does not seam the related, adjusting that made no difference when the hammer was failing to cock.

The other trigger assembly I pulled comparison required no adjustment when re installed, I do not remember ever needing to re adjust after removal and install.

Have I been lucky with the others, or is this a potential problem starting?

Just found these photo from when I was fighting my trigger.  Its an original.
1. Unset trigger, if the spring is in place the nose of the sear will be up and against the hammer when cocking.
2. This show position after a set trigger is tripped.
3. Sear tripped by pulling just front trigger. Exaggerate.
4. Assembly in set position. Sear nose should be up.
5. Original hammer
In theory, set or unset the back of the sear should not contact the triggers while being cocked. If it does it may engage the half cock but not the full cock.   

Also imagine the sear binding in the frame enough to over come the spring pressure and hold the sear away from the hammer, at that point the hammer would not cock either.