I have a bit of experience with Spiridinovian style through my study of Kadochnikov style. I don't really want to discuss the specifics here...
AI Retuinksih, who was a Kadochnikov style student of, I think, about 17 years, wrote that Mr. Kadochnikov was pretty much the only person who ended up making Spiridinovian style 'work'.
Spiridinov's style was called 'Officer's style', taught mainly in the officer ranks (whereas other's learned the other forms of Sambo), and was for the 'saboteur.' Remember, a lot of the system's were not taught to regular military, they weren't belived 'smart' enough to learn them. Mr. Kadochnikov's system for a long time was taught at the Rocket and Engineering schools because they were easier to teach.
It's based in old Russian Tsarist and before methods, and some eastern methods mixed in (he studied Aiki-jitsu and others and put it in his part of the development of SAMBO). I think most would find it the most 'soft' of the styles of Sambo because he couldn't get down and roll around with everyone. Sambo had three flavors, one sport, one military and police, and one for the special ops-type saboteur who couldn't bother wrestling aruond for a while. Spiridinov's style, was the last one mentioned. It's for the most part pretty practical, but on the other hand, needs a lot of traniing to pull off.
Mr. Kadochnikov at one point was a student of two of Spiridinov's direct students (one of whom still lives in Moscow but is in his 80's and still full of piss and vinegar

).
The methods in Spiridinovian system are based a lot upon methods that revolved a lot around redirection of energy, shots to the throat and disabling methods, etc. Not a lot of dancing about....
His is probably the hardest to learn and use, because of his personal body that he designed it around...he was injured in war by a bayonet and generally of poor health. So, he designed his system to use very little energy to get the job done.
Mr. Kadochnikov completed a lot of that work that was 'hard to do' by his more indepth study of biomechanics and mechanics which made a lot of the method used more clear in how they functioned.
After Kadochnikov, you don't find a whole lot of active study of Spiridinovian style because he made it much simpler to use and learn. I don't think Retuinskih really touched on Spiridinovian style in the development of ROSS, and studied mainly in the other forms of Sambo and put those together with Kadochnikov system and some native Cossack and Slavic methods and dance to form ROSS. I have my own opinions on dance in the development of RMA, but that's another conversation....
I still sell the manual on a very limited basis to RMA students because it's part of American RMA works, and feel it's better than some of the manuals in Russia...though it pales compared to the PraMek manual that will come out.
As for ROSS in America, I hope it comes back, as some of those folks teaching it in the late 90's and early 00's when I was studying ROSS were really great and nice people who worked really hard to get ROSS going.
Sonny has a great point about all the ones we don't see...I personally feel that had it not been for the Soviet ideology, it would be evident RMA is as big as CMA.
M