If you use Starsan correctly, it works fine. It's not meant to be stored, so I would guess that is the source for some peoples problems with it.
The mold on the inside of the neck of the carboy is a somewhat typical thing in aged sour beers, especially if you have dried krausen on the inside there. You are likely to find people who sanitize with iodine who have had the same experience. The issue isn't likely the sanitizer, it's likely either a problem with cleanliness or the lack of oxygen control in those airlocks (via vacuum usually, or a bad seal). StarSan only sanitizes clean surfaces, and air from the environment getting into sour beers creates all sorts of problems from mold to acetic acid/ethyl acetate and THP.
I use BetterBottles with DryTraps and have never had an issue with mold in 7 years of making almost exclusively aged sour beer. I haven't used any type of sanitizer whatsoever in the last 4-5 years for my carboys unless I am switching up to a new culture, which is rare because I tend to use the same cultures (I blow through a lot of PBW though to make sure things are clean). I think the DryTraps are no longer in production though and I've heard that finding them now is difficult. You might want to think about moving to a keg with a spunding valve on it for long term sour aging.
As a side note, I know that the idea that StarSan doesn't kill various microbes is a fairly widely adopted thing around here, but in this case there is evidence to be skeptical of the authoritative sources on this claim (as well as a lack of evidence for authoritative sources that do claim it, like food science sources). If you want to read up more on that, we have a section for it on the MTF wiki on the Quality Assurance page with references.