I employed this lock on my personal Jaeger rifle, and it served me very well for many years. But over the course of time, I tinkered with it to make it better, so here are some of my observations.
First, I used 7/8" flints. That's 7/8" in length not width. I shot them bevel up and bevel down, according to the way they looked when clamped in the jaws. Of note, particular to this thread, the gap between the flint and the frizzen needs to be as close as you can get it, without interfering with the frizzen closing on the pan. With my own rifle, I had issues with the flint striking the pan when I set the flint close as I've described. So I did something quite radical. I clamped the tumbler in a machinist's vise, heated the tumbler axle red with an Oxy/acetylene torch and rotated the axle back a few degrees. After this treatment, the flint no longer struck the pan. The same effect might have been accomplished by adding a shim of steel to the inside shoulder of the cock where it strikes the top of the lock plate at rest, thereby impeding its forward rotation.
I never had issues like the op with the frizzen not fully opening. On my lock, the frizzen snapped open when the pan cover was about 3/8" off the pan. And it never rebounded - ever. If I was dealing with your lock, I would file on the top leaf of the frizzen spring some, then re-polish, to reduce the force it applies to the toe of the frizzen. Balancing the springs, is likely all this lock needs. But move the flint forward in the jaws until it almost touches the frizzen face.
My lock threw sparks like a cutting torch, and the rifle accounted for many honours in competition, and many heads of game including mule deer, black bears, and moose. It was the perfect hunting rifle.
The first picture I took while I was moose hunting, and was a little bored waiting for Bullwinkle. Notice the flint is well worn (but trusted) and the bevel is down. The second one is in my back yard, and shows the flint bevel up. You may see damage to the pan in this shot from the flint striking the pan. The flint leather in both pics is from the cuff of a work glove. The leather needs to be thick enough to mold itself to the nuances of the rough flint, grip the teeth of the jaws of the cock, and cushion the blow to the flint as it strikes the frizzen.