Here's how I do mine. The fir block is harder than a standard 2x4. Drilled 5/8" The barrel did not wiggle much. Pretty close fit. The block is securely clamped. Used the quill for a press. Little brass block went against the safety. Was easy. Works perfect. Remember the old purple/blue Craftsman machines? 1939 vintage. You should be able to improve your trigger some IF and I said IF you are already in the ballpark by turning very small increments to the screw. Don't try to get it too light where it goes off too easy. It's not a Rekord but can still be very good. 

Last picture shows the stock after I improved the color and finish. And the muzzle brake I made that does not add length to the barrel.

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Set up so the quill is extended most of the way when it releases the spring tension. Then let the quill up until the preload is gone. You must make sure your setup is secure so a badly kinked spring can't cause a problem. Notice the wooden block is clamped to the table with strong machinist clamps. Through bolts would work.

Maybe I'll post some machinist playground photos . I have 2 very nice South Bend lathes, a nice Logan metal shaper. a Burke #4 horizontal milling machine with vertical attachment, an Enco 6 x 26 vertical I bought from the original owner c1979, a handy Grizzly 1007 column mill/drill. Several 30's to 40's vintage drill presses. Bench and column.

I'm having fun with a young man lately who I helped acquire a Crosman Mendozza 177. We're making a steel replica of the older Beeman muzzle brake. He's taken an interest in operating a lathe. A really good kid. I'm happy to share with him.