As soon as you mentioned that the leade was rough looking I placed a bet with myself that it would be a CZ barrel.
They're noted for hit or miss barrel quality. I've heard it said that 80% of their barrels are "average" for accuracy, with 10% more being "outstanding", and the remaining 10% being "poor"
The usual cause is dull chamber reamers pushed beyond their best service life or poor machining practices.
Yours falls between average and poor from what I can see. Typical CZ. I doubt they'll do much for you warranty-wise.
If they did replace the barrel, the one you get might be more of the same. Highly unlikely their warranty dept. has a supply of "good" barrels for customers that complain about the originals. It's hard to make money that way.
I've owned several CZ rifles, the only one I have left is a BRNO 2E. It's got a good bore and shoots well for a light barreled rifle.
There's not much you can do to make the barrel you have now shoot well. Lapping won't fix the poor machine job, it'll just make it smoother. Having said that, it might help a little. That smeared leade isn't going anywhere unless you cut the barrel off and re-chamber it properly.
A few years ago, the CZ forum on RFC had a lot of threads on making the rifles better, the general consensus was that a good aftermarket barrel was the best place to start.
As for the bottom of the bore looking rough, I believe it's caused by the "ground glass", for lack of a better term, that's used in rimfire priming compound. It falls to the bottom of the bore after each shot, then gets dragged along by successive shots, leaving tiny scratches in the steel. The bottom of my 1970 Anschutz 54 bore looks like it's been sandblasted. That rifle shoots very well with God knows how many rounds through it. I'm at least the 3rd owner.
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I also have a Tikka T1x with about 8-9000 rounds through it that shows the beginning of the same phenomenon. Another good shooting rifle.
Other than the BRNO, which is no spring chicken either, I've given up on CZ as being too much of a gamble of getting a good shooter.