It almost sounds like you have several small issues going on rather than pin pointing one big issue.
Absolutely clean everything, a Lewis lead remover or a piece of Chore Boy copper scrubbing pad (copper steel wool) put on a bore brush will work. I like the Chore Boy & have used it for years with great success. I just put a big wad of it on the end of a bore brush & screw the bore brush into a piece of cleaning rod (no handle). Then I chuck the piece of cleaning rod up in a cordless drill. I clean the cylinders & the forcing cone this way, it cleans them in seconds.
Once you get everything clean you should slug ALL of your cylinders & you bbl. When you slug your bbl go slow & feel for tight spots. Especially where the bbl screws into the frame. The cylinders should all read the same dia. & the #’s you get should help you narrow down your leading issues.

A couple of things to think about:
.007” is at the far end of the specs & can cause problems if there’s any movement/slop in the timing of your revolver.
Once lead starts to build up in the forcing cone it does a snowball effect & worsens rapidly. IE, the more the dia. Constricts the more lead it shaves & the more lead gets deposited per shot.
The hotter (pressure& speed) the load is the more it has to conform to the specs of the pistol. Light loads are forgiving & will mask reloading issues that heavy loads tend to bring out.

I’ve owned a 586 since 1987, bought it new & it has been my primary 38/357 revolver since then. After shooting countless 1000’s of rounds in it I had to send it back to S&W to have them rebuild it. I shot that pistol enough to wear the timing out. They rebuilt it & recut the forcing cone for me. Just recutting the forcing cone does nothing if all the pistols issues aren’t addressed. A 1/1000 of here & 4/1000 of their add up to trouble.

On a side note, that 586 always did shoot different with full house 357 loads. I would size the 38spl & light 357 loads to .358 & never have a problem. When I’d shoot/load full house 357’s in it I’d have to size the bullets to .357 or leading would occur rather quickly in the forcing cone area. One of my all time favorite powder/bullet combo was WW820 pull down powder & the Lyman 358311 bullet. I used to order 4 8# jugs of that powder at a time & shoot full house loads (13g) by the 1000’s. The cylinder’s dia. was tight in that revolver I’d get leading problems only with full house loads. When I dropped the bullet dia. to .357 for the full house loads only, the leading issues cleared up with the full house loads.

Let us know what you find & good luck.