I know you were asking specifically about the South Bend 9s, but it seems like you are mostly interested in more accurate than your HF 8x18" without going to a much larger lathe.
You might consider an older toolroom lathe, there are several small toolroom lathes from the 1920s-40s that were very high quality, small and because of their intended use as a specialists lathe, often not totally used up, so long as they didn't end up under a tarp in a field.
Because they are a little odd, and small, they are often fairly cheap when they do turn up. Most have threaded spindles with odd threads, or are collet based like a watch makers lathe which also turns some off of them, helping to keep the prices down. Mostly though people just don't know what these lathes are, lots of people just look for the names they recognize, South Bend, Logan, Atlas.
A plus to the change gear ones, is they often have a much wider range of thread options than you typically find on more common lathes.
Many were also offered as a simpler precision bench lathe, still very accurate, but without thread cutting so you do need to make sure you know what you are getting (these are pretty obvious by the lack of a lead screw).
The downside is parts are very limited, DIY or find a parts lathe to cannibalize. Many are in the 7-11" range with around 20" between centers. Replacement factory parts and tooling can be $$$ due to rarity.
Pre-HLV Hardinge made their Cataract lathes in 7, 9, 11 and 15" sizes, the 7 / 9" and 11 / 15" were the same lathes just with riser blocks to increase swing. I've seen these pop up occasionally in the $700-1000 range.
Cataract lathes
Rivett was a competitor of Hardinge, they made 8, 9 and 10" tool room lathes.
Rivett
Wade is another, they offered an 8-1/2x24" tool room lathe. I've only seen one of these for sale, but even with a quick change gear box they were only asking around $1000.
Wade
All of the above were US companies.
Schaublin is Swiss, very nice lathes, but being Swiss and known to more people usually not so cheap. I have seen a few nice ones turn up in the $2000-4000 range which with many of the current 9-10" lathes running $2000-3000 really isn't too bad.
Schaublin
There are others, but these are some that I know of and have seen at ;east a few of for sale over the years.
South Bend did offer a "Tool room" version of the 9A. This was basically just a standard 9A finished to a higher standard. No idea how you would tell one apart from a standard model 60+ years after it left the factory. Seems like a lot of sellers like to call any smallish vintage lathe a toolroom lathe, along with rare, and one of a kind.
Still if you were able to find a legitimate tool room 9A it should be a cut above the regular models.
I stumbled onto a Rivett 608 (8-1/2x 21") from 1932, in great shape other than missing the motor set up. It is a project, but other than having to figure out a new motor drive, it came with a good amount of tooling, is in excellent shape and is a pleasure just to fondle while I try to get it running again. It is quirky with a 1-5/8"-14 threaded spindle, uses a weird proprietary (and very expensive) collet set, and is a change gear lathe but the price was right and it should be far more accurate than my skills.