When you say 'runs out of adjustment', do you mean the tool holder itself bottoms out as low as it can go leaving the parting tool tip still too high relative to stock center? If so, by about how much is remaining? I've heard of this issue on certain import lathes where their compound sits abnormally high relative to 'typical' lathes of the same swing. So even though you purchase the recommended tooling set (250 series in your case) based nominal swing, all bets are off if the datum (top of compound) is sitting high because the tooling just stacks on top of that. The example I saw (cant recall exact model, Craftex or Busy Bee.. basically one of the rebranded import lathes) had this exact issue when swapping in a more modern adjustable tool post.
One guy was able to trim material off the toolholder bottom without sacrificing too much rigidity, but I don't recall if it was a parting holder. If you were 'pretty close' on tip height, say 0.1", you could notch out that from parting blade as long as its not a T-profile. This is not optimal at all though, loss of blade strength by reduced net height. Another option might be to get a straight shank insert type tool holder. hey inevitably will be thicker shank that what your toolholder will carry (example .75 or 1.0" shank vs say 0.625 toolblock gap). But what I've seen is people do is partially mill the tool shank to fit the lathe & correct the heiht issue correcting 2 problems in one shot. The good toolholders might be tough material, but the Asian knockoffs might be softer.
I'm not sure if this helpful, or your exact issue. IMO the tool holder suppliers should really provide a sizing sketch that correlates the vertical height from top of compound to lathe center & not rely on 'swing' which just confuses matters.