Howdy! Just joined as I am in search for someone/somewhere who could manufacture SS profiled caps for me. I know it’s a long shot but I guess still worth at least a try.
Apparently I can’t post link to the picture here but SS looks a bit similar to SA profile but is still distinctively different. Anyone? Anywhere? 
Are you by chance referring to Leopold’s SS2 (step sculpture 2) profile? I’m not familiar with SS, but that doesn’t mean it’s not a thing.
If it’s the former, so far no one that I’m aware of has manufactured a set of caps with their profile. Probably because it’s pretty close to Cherry. Leopold is very stingy with these caps as well, frustratingly so.
As mentioned I can’t link to the picture, but I tried to search for Leopold’s step sculpture 2 and I can’t be sure as I couldn’t find profile drawing / sideways photo except one or two, which didn’t tell me anything conclusive. I think this is not the same but if anyone is familiar with the Leopold’s profile then the one I am looking for can be found for example by entering “SP SS Profile Keycaps w/ Futaba ML” into search engine and finding link to “deskthority dot net” probably on the very top. Going there, on the bottom of the page, there is a drawing showing “SS Family” and some photos a little higher
Oh, I see, yeah, those are something entirely different. Not one I’ve personally seen before either, or maybe I have and simply don’t remember them among all the rest.
Reading that thread it sounds like these are rather unique. The profile was developed by Signature Plastics and it sounds like their molds are retired and likely lost. So my guess is your best bet is to find something similar.
@Andreas has made a profile that is spherical and sculpted. It’s in the interest check stage at present and if you’re curious, here’s some more information: URSA Keycaps.
Those were popular in the 80s’ machines. I am not sure who developed them in the first place but it is true that SP had them once in their programme. Alas, not anymore 
And yes, I asked them too. The URSA caps you mentioned look similar from the top but those positive angles don’t seem to be there. I wouldn’t be too precious about it being a little different but SA for example is 12 deg difference
I think your only option would be to 3d print the profile. Especially since it seems most of the old ones out there didn’t fit on MX stems anyway. I have no experience with 3d printing, so I can’t offer much help there.
I guess you would have to recreate the dish from looking at images and guessing. The sculpt and height could be figured out from the illustration comparing them to SA