It's a bit hard to tell. Looks like the adjust wheel looks grimy tried to zoom the picture but it's a bit blurred. What I would do is put the stem back in and check the enguagement to see if it engages smoothly and isnt binding. Check the squared end of the stem to see if the corners haven't been rounded.
I have stripped down the movement completely and will check and re-assemble it tomorrow. Here's a pic of what the stem area looked like. Notice anything wrong ? I'm a newbie with quartzes so I certainly don't.
The additional jewels for the 24 jewels movements is for the auto winder, so shouldn't effect the loading of the gear train. The balances I believe are all the same, with some receiving additional adjustment for chronometer grading. I wonder if the GR reference is made from measurements of original springs fitted, and perhaps Omega updates them over time? Perhaps the metallurgy of the springs changed through the years, although all would be white alloy. The GR catalogue also quotes various springs for the Cal 26X range, but I believe these should probably all be the same. There's an argument that running a centre-seconds hand adds to the load (it will typically reduce amplitude by something like 5-10 degrees when adjusted) but that's not enough to significantly affect performance.
I see that on the Cousins website they list three different springs if you search for a Cal 565...
On my Cal 552 I have a 1.10 x .105 x 360 (11) spring which reaches 300 degrees amplitude, if that helps.
The watch has been returned to the customer. You are correct someone had been poking around with this movement most of the screws were very badly bruised the hairspring had been badly damaged & the balance staff broken.