OP, there is a bit more to it than Ganderite is typing.
The metal fouling goes on first, them the gasses and powder residue go on. This is repeated with every shot. Some people think the carbon fouling gets pushed out by the next bullet fired. Not so. That carbon fouling is very hard and mostly just gets impregnated into the previous coat of jacket fouling.
Sweet's 303 is very aggressive and it's intended for harsher jacket fouling than the modern copper composite jackets contain.
Usually the layers of fouling are very closely associated with how many shooting sessions the bore goes through between cleanings.
I've had rifles come in that were never cleaned from the day they were purchased. One fellow recently brought in his father's Model 1600 Husqvarna, chambered for the 270Win. He also brought in every case, for every bullet that had been shot through the bore from after his father purchased the rifle new. There were 16 boxes of factory cases. Everything from old CIL and Dominion to Green box Remington and recent Federal Premium.
The old boy gave the rifle to his son and explained in a very factual manner that the bore must be worn pretty badly because it would no longer shoot minute of Deer chest out to 150 yards. That was the distance from the house porch to the vegetable garden.
That had to be one of the most fouled bores I've had the privilege to admire.
The fellow that brought it in wanted to rebarrel it in the original cartridge and wasn't worried about the cost. It was a family heirloom in his mind and he wanted to preserve it.
I mentioned it only really needed a good cleaning. I also told him it wasn't going to get clean on it's own and if he wanted the job done, I would take the barreled action out of the stock and apply the first few coats of very aggressive cleaner, then he would be responsible for the rest. He sniveled a bit, mostly because he just wanted to shoot it and not worry about anything else. That's when I mentioned how much it was going to cost for another barrel or the hours it would take to clean it properly. Likely most smiths wouldn't even want to take on the job. Not enough money in it to make it worthwhile.
First, I plugged the chamber, then filled the bore with Sweets, then set the rifle aside for half an hour.
After pouring out the Sweets, I ran a worn out 270 brush through the bore. There were actually little slivers of copper that were visible on the rag placed under the muzzle. After this, you could see the shiny fouling still in the bore. Repeated this half a dozen times. Each time, it removed at least one layer of fouling. Ok, clean out the Sweets residue with acetone, then alcohol.
Next, applied a coat of Wipe Out and let it sit overnight. This only revealed yet another layer of fouling.
The owner of the rifle came over, hoping that he didn't have to do any work. I showed him the results and he was seriously considering a new barrel install. He knew absolutely nothing about how to clean a bore or when it was necessary. He got a quick lesson and asked if he could borrow the tools and cleaner to take home with him for the weekend. He used up a whole bottle of Wipe Out, ruined another brush and went through a whole bag of 250 patches. Somehow he had missed that the solution needed to be allowed to sit between wiping.
However, he did get a lot of the fouling out. I sent him home again with more Wipe Out, patches, brushes. He used his big head and came back a few days later with a relatively clean bore. He was impressed with his accomplishment. Works as a teller in a bank. Anything that doesn't have a keyboard is to be shunned or feared.
We then proceeded to finish the job with JBs and this time he not only paid attention but showed some enthusiasm.
After getting the bore clean to the steel, we took the rifle to his Dad's place to sight in. Of course the first shot was a flyer and I had to explain why. Also had to explain why he shouldn't keep shooting and allow the barrel to cool, so that every shot he took while hunting would be the same as when he sighted in. Not many Deer will stand and waif for anyone to shoot a string to heat up the bore and settle down harmonics.
After four fouling shots, the rifle settled right down and groups very slightly larger than moa were shot from a cold bore. After around 25 shots, the group started to open up again. He got upset, until I pointed out that this was perfectly normal and indicated it was time to clean again. He was devastated. He envisioned a rehash of all the effort he had just gone through.
I had my portable gun vise with me, as well as the bottle of Wipe Out and cleaning products. Two treatments of Wipe Out over an hour and the bore was back to bare metal. He was very happy with that. I explained that he would have to go through the fouling process again and not to mess with the Weaver K4X Steelite settings. When he bought the last batch of ammo, he purchased a case of ten boxes, so all were from the same lot and should shoot the same unless something goes awry.
He's gone through over a hundred rounds since the first sight in and has had to clean appx every 25-30 rounds. He's happy. He went to the local gun shop, picked up a Tipton vice as well as all the tools and cleaning supplies he would need and to replenish the materials he had used of mine.
He wanted to give me a couple of hundred for the job and info. Nope, I've known his father for over 60 years and he's a decent sort that would have done the same for anyone.
OP, I can see from your photos that your cleaning issues don't require more than a good cleaning with Wipe Out. The people that make Wipe Out state that it can be left in the bore as a preservative. That's not something I would recommend.