Looks like a great project for that price. Always good to see one put back in to service.

The first falling block I bought was a Hopkins and Allen 44 rimfire about 50 years ago and was unable to find ammo for it. After looking for a couple of years I gave up and sold it. But the bug had bit me and now I have about 26 falling block rifles and I never get tired of shooting them.

The factory lever spring is strong. Make sure the spring screw is holding the spring tight against the frame. Someone may have replaced the original spring with a wimpy homemade one. Also look at the roller in the lever that rides the spring. Making a slightly larger diameter roller can tighten up the contact.

Make sure the barrel is seating all the way back in the frame. Excessive wear or damage to the tip of the takedown screw or to the barrel recess the screw engages can sometimes let the barrel shift slightly forward away from the block, allowing the block to flop around in the mortise.

Some time back, I made a few new oversized blocks to obtain a proper snug fit in three H&A Juniors that showed up about the same time, but I won't make the blocks again. The dimensions of the three mortises were all over the place, and to fit correctly, the blocks had to be cut to match each frame's mortise individually. 

I did make one of the blocks for centerfire, and ended up with a fun Junior in 32 S&W Long, to use as a companion piece with a small frame Smith & Wesson in the same chambering. 

Also made a different extractor for that rifle that was actuated by the roller in the lever, instead of by the breach block, which increased the range of motion for extraction. 

It was a fun single-run exercise, but once was more than enough to satisfy my curiosity.

Using the action you show pictured where the extractor screw and lever screw are positioned close together (not the H&A actions where there is greater distance between the screws), make your exctractor with more material extending toward the front of the action just above the pivot screw, so that when your lever is rotated almost fully forward and the roller in the tip of the lever just begins to touch the bevel on the lever spring, the roller touches the extractor.

Since the original spring is a strong one, when the roller then quickly ramps across the rest of bevel of the spring, the roller then imparts a slight "kick" to the extractor which can clear a loaded round from the action. The timing of the contact is important for this to occur.

Also by adding material to the front of the extractor under the hook, you can then remove material from the rear of the extractor (against the block) under the hook, which allows it to rotate slightly futher rearward, increasing the range of extraction.