Ok that looks correct. I just wanted be sure the spring was the correct size/diameter for your guiderod although it looks to be a coil short. For the 4516-1, the factory S&W spring was a 20 coil spring rated at 16#. You will find however some 4516-1s with a reducing bushing in the slide and fitted with the nested spring set found in the 4516-2. For the guns with the single spring like yours, and mine for that matter, we are relegated to the aftermarket for replacement springs since S&W doesn't make the 4516-1 spring any more. IMO the dash1 guns, were a bit undersprung from the get go anyway.
Any idea what weight that spring you have is rated at? Factory is as I said 16lb. From what you described originally I think your new spring is too light. I'd suggest getting a recoil calibration pack from Wolff and try out the heavier weight ratings and see what your gun prefers for the loads you're shooting.
In the meantime since the gun obviously doesn't run right with the new spring, I'd stick the old one back in there for now.
Alternately there are two other options for a long term fix recoil spring.
Option one... You can have a reducing bushing machined and installed in the slide then fit a 4516-2 recoil assembly which consists of a thin guiderod and two counterwound springs nested one inside the other.
Here's that bushing
And option two... A reduced diameter guiderod coupled with a ISMI flatwire spring. For this you need a solid stainless one piece guiderod either turned down and shortened from another part or machined from scratch.
For the record, I went with option two on mine.
Hopefully I've been of some help.
Cheers
Bill