pellet spiraling

"FastEddie"I you zoom in the end of the barrel (crown) it doesn't look perfectly round. It almost looks hexagonal.

Or am I seeing things?
That is a normal ST barrel. It should have what appear as 5 "flats" and 5 "corners. The crowning tends to accentuate the appearance.
When shooting be very disciplined with your "follow-through", holding the sight on target as best you possibly can as, during and after the shot has been made.
When the .25 started to become more popular back ten years ago, shooters claimed the caliber was less accurate than the .22. After I became the first to shoot sub inch 100 yd groups with a .25 and showed those , suddenly the .25 "seemed" to be OK and as accurate.
Shooters just settled down to give the same attention they would to a springer and the rest followed.
Now I see similar with the .30 and .357. Very few sub inch 100 yd groups have been shown yet. The rifles need to be treated with all the care given to a springer,especially trigger control and follow-through. Another age old habit is the famous "cheek weld" putting side pressure to the stock where it is not wanted. Eliminating a cheek weld will often reduce the number of lateral fliers in a group.

As for your spiral problem: anything that shaves or marks the lead on one side will cause it. I can deliberately produce predictable fliers by marking the heads and to some extent the skirts. Then by indexing the loading orientations can nominate the direction the flier will impact; even make them group very acceptably to 70 yards by synchronizing the spirals so that the pellets arrive at the same spiral "clock" position. So, your thoughts on the possible thimble to steel anomaly seem a good place to attend. However I would be VERY VERY careful about doing anything other than normal cleaning of the barrel every 50 to 100 shots. 
If you clean the barrel (dirty barrels cause spirals - a LOT of felt cleaning pellets went through the best barrels DURING 25 shot cards at the recent World Benchrest Championships, and thorough cleaning between cards) then look through it at a light area, you will see concentric circles all the way down the barrel. These are reflections. The circles are true and concentric because every barrel is inspected by Fredrik for straightness at the factory. If the reflected circles are not right, the barrel is re-straightened and or rejected.
So take great care when you are polishing that ST barrel ... JMA ... Best regards, Harry.
 
You can also use a QTip in the breech end and see if there are any burrs and at the transfer port. Inspect the breech oring. Inspect the push rod pushing the pellet into the breech. Push another pellet through and carefully inspect the pellet with a magnify glass for uniformity. The pellet should be evenly marked from the rifling and the skirt should be even all around and at the back of the skirt. Hek, I've heard peeps shooting into a 5 gallon bucket of water to inspect the pellets going thru their barrel. Ted did just that on a ladder. 
 
"Dartagnan" I've heard peeps shooting into a 5 gallon bucket of water to inspect the pellets going thru their barrel. Ted did just that on a ladder. 
I did the original research into water testing in 2003.
Please see the post I just cobbled together from a small portion of that research. It is in the General Airgunning section. Plenty of pictures.
Questions are welcome but remember I am in a time zone about 14 hours displaced (ahead) of USA.
Note all my tests were shot horizontally through water - even so penetration for round head best BC pellets was 5 ft and further.
Kind regards, Harry.
 
@FastEddie don't touch the barrel unless 100% necessary. The barrel on mine looks exactly like that. I removed the shroud on mine but left the compensator (the metal part screwed at the muzzle end with an O-ring on it) as is on the barrel and shot at 50 yards. The gun shot less than 1/2 inch group. As soon as I put the shroud back on the gun, the group widened to 2 inches. No I was convinced that the shroud has the issue but then on close inspection I notices that the compensator had very minor clipping marks on it. I still don't understand that why the gun shoots perfectly without the shroud but looses accuracy when the shroud is put on it while the pellets clipping the compensator in both cases.
 
Try shooting it without the shroud, moderator ,etc. Just the barrel. If they don't spiral anymore than they're probably clipping. I had this problem. I drilled the airstripper and endcap a little bigger till it stopped. I also had a problem that the pellet probe was seating too far deep into the breech crushing one side of the pellet skirt. Load a pellet then push it back out and inspect the skirt.