PRS SC enabler here...
I've had SC245, SC58, Stripped 58, and older Singlecut models; these days I'm playing a McCarty Singlecut Artist Relations guitar built by the PS team. Here's my take:
I'm a believer in the 2 piece bridge. I think it lends more of a woody, vintage vibe to the Singlecut model. For me, that would be an important starting point, and given your stated preference, might make the Ted a little less appealing, though I've played some Teds that did sound very close, and some that to my ear sounded a little more modern than the models with the two-piece.
The Ted will be nitro, I believe, and the others V12. In terms of tone, the SC245, SC58, and Stripper are all cut from the same cloth in terms of tone. Good cloth, by the way. They sound great. I like the fingerboard binding on the SC58 and new SC245s, but it doesn't affect the tone, so you may or may not want that.
The McCarty Singlecut is the most vintage-sounding SC yet, by a pretty substantial margin. However, it's not in your price range and the others are. The differences with the McCarty Singlecut are the slightly thicker body, the nitro finish, some of the woods selected, the specially wound 57/08s with a more vintage wiring setup, and some of the fancy doodads. I haven't seen one on the used market, but you might want to keep an eye open.
What I'd do is find a great sounding example of one of the other models, and see if the PTC can replace the pickups with the specially wound ones (I don't know if they're available through the PTC or not, but it'd be worth checking IMHO, as they do give the guitar a heck of a fine tone that's more on the vintage side).