Leave the 14 lbs. rebound spring in place, that has NOTHING to do with the power generated by the mainspring. It also has almost zero effect on the trigger pull in Double Action but does reduce the Single Action trigger pull from 4 lbs. to a bit over 3 lbs. What you need to do is put the factory mainspring back in place, that is directly linked to the power generated by the hammer strike.
Now, for properly tuning the 625 JM. You really need a trigger pull gage of some type, going by "feel" just doesn't cut it. I prefer the Lyman Digital trigger gage but that is a 65 dollar purchase and I can understand why you wouldn't want to spend that much. Look around at Midway or Brownells and you should find a basic spring scale gage in the 20-30 dollar price range. If you shop at Brownells I would recommend purchasing some spare Strain Screws because you will need them. BTW, I prefer the black steel screws because I've found that the stainless steel strain screws are softer and will peen shorter at the tip in only 1500 rounds fired. Once the tip of the strain screw peens over enough to reduce the trigger weight it becomes a distinct hassle to remove because you have to remove the mainspring and file the resulting burr down using a tiny needle file with the screw in place.
One item I recommend you install is a Cylinder & Slide Extended Length Firing Pin. This will increase the firing pin effective length by about 0.015 inch and allow reliable ignition with a lightened trigger with or without the use of moon clips. However it should NOT be used with the original factory trigger pull of about 12.5 lbs., you really need to tune the trigger to 9.5 lbs. or less to install this firing pin. Because with the original factory trigger weight there is a distinct risk of a pierced primer.
Tuning. Install a 14 rebound spring and then shorten the Strain Screw enough to reduce the Double Action trigger pull to 9.0 lbs. using the original factory mainspring. Filing the tip of the Strain Screw so that the overall length is shorter by about 0.020-0.025 inch should get you into the 9.5 to 10 lbs. ball park. Once at that point you then need to work it down to 9.0 lbs. in increments of just 0.002 inch. Yeah, it really is that sensitive and you'll now understand why I recommend having some spares on hand. You'll also understand why I prefer the black hardened screws over the stainless version.
Note, you can go lighter than 8 lbs. but that will require taking steps to minimize any drag on the hammer that might reduce the power of the hammer strike. I would suggest shooting at least 1500 rounds through the revolver before attempting this because any areas causing drag on the hammer will show up as rub marks in the frame recess or sideplate. You can then make up some tiny shims to re-position the hammer using 0.001 or 0.002 inch thick shim stock. BTW, the easiest way to put a hole in shim stock this thin is with a diamond burr in a Dremel. Second easiest is using a drill with the shim clamped very firmly between 2 pieces of hard maple or oak. Once the hole is drilled you can then trim the shim using basic paper cutting scissors. Note, total shim thickness should NOT exceed 0.003 inch because putting in to much shim will start causing the hammer to bind when the sideplate is tightened down.