While there were a few (CONRAIL & export) .38 686s made. Even if a cylinder was still available, it would be $$$ to have it fitted properly.
As suggested, proper cleaning will eliminate the carbon ring issue. When (infrequently) I encounter them, an overnight soaking with Kroil followed by the aforementioned .40 cal brushing does the trick.
If you reload, its easy to assemble mild range/target loads (even full wadcutters) in .357 cases, thus eliminating the issue altogether

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-jwk-
US Army '72-'95