Ziggy, as I looked at the photo of the frame and differential I could not tell if the diff was mounted onto the frame or the frame was just set over it.
What you have looks to be just the factory live axle/differential with stamped steel control arms for a regular Mustang GT. If that mounts to your frame, you can just go to a salvage yard and get whatever parts you need from a Mustang GT. That would be the best, IMHO, because factory parts are readily available and inexpensive compared to specialty parts. If the assembly does mount onto your frame that means the kit was engineered to use those parts...if it doesn't you'll have to go about getting a differential assembly mounted, and that can mean fabricating custom bar-mounting points on the differential as well as on the Street Beasts frame.
Here's an idea if the parts do fit onto the frame you have...there is a company named Factory Five Racing (FFR) who makes a kit that is designed to use the Mustang as a donor, so it is engineered to use the parts you have already. If you contact them they may be able to give you some idea about springs to use, what spring rate, that sort of thing---and you may be able to buy the parts from them, as I think they sell their wares to anyone needing go-fast parts for the Mustang FOX/SN95 based products. If you are interested in improving your kits handling and ride, there is the option to replace the factory control arms with tubular ones from FFR...and perhaps the option to use coil-overs as well. I know you stated a preference to use the factory parts due to budgetary issues...IMHO it will all depend on whether the kit was designed to use the factory diff/control arm assembly or not.
My kit has a parallel 4-bar rear suspension with a Panhard rod. When I bought the car the urethane bushings were so brittle that they fell to pieces within 500 miles. It too me over a year to find replacement busings...but when I did find them the repair was inexpensive and easy. My chassis was built by Ron Godell Racing out of Tulsa, OK and was engineered for the setup I described....there's no telling what your Street Beast chassis was engineered for unless you can find a build manual.
Just a historical perspective....Street Beasts was the Phoenix that rose from the ashes of a different component car manufacturer. There may be others on the forum who have cars made by that defunct company and can help you. Perhaps a web search will yield the information regarding the "parent company"...as I recall the end of the parent company was not pleasant, with many paying customers not getting things to which they were entitled...but Street Beasts attempted to resurrect the product line. I could be wrong about all this....after all, at my age the memory isn't so good, so if you find out that the history I mentioned is not accurate, I apologize, I'm just trying to retrieve long-ago acquired information that was not really needed, so perhaps not remembered correctly? If you do find the parent company...check out the "manufacturers" forums to see if there might be a brand-specific forum.
[EDIT--I surfed into your profile and see that you have found the information to which the previous paragraph referred. CMC...if you'll look in the "Manufacturers Forums" section I think you'll find a forum for CMC products...if so I'll post a link. Good luck!]
I don't really think this is the company, but it's the closest I could find in the Manufacturers' Forums....just don't be surprised if it isn't the company from which Street Beasts arose...I think the Contemporary Classics are quite highly engineered, well built component cars in high demand...IIRC CMC (the company from which I believe Street Beasts arose) stood for Classic Motor Carriages. Anyway, if you'll read a few posts in this forum you'll figure out if CC and CMC are different, as I suspect is the case:
Contemporary Classic Forums - Club Cobra
Good luck...getting what we call a "basket case" means getting a frame with a "basket" of parts with no instructions...kind of the situation in which you find yourself and we all know how difficult that can be, so keep posting and asking questions.
Cheers!
Doug