Well I don't see anything so flammable here lol
Anyway, what you said is true plus I'm quite certain the S and MS had the mig-21 like cockpit, now the only thing I'm not so sure about is the 23M cockpit, I could swear I saw a picture of it without the "radar-on-hud" but...it wouldn't be the first time I'm wrong lol...
Anyway for major MiG-23 variants:
S - basically preproduction model(S stands for Sapphir radar from MiG-21 btw.)
M - first mass produced
MF - significantly crippled "M" exported to Warsav Pact countries ONLY
MS - insanely crippled "M" intended for export to non-WP countries(Arabs,Africa etc..., notice the "S")
P - interceptor version
ML - massive avionics updates, engine updates, reduced weight and improved airframe
MLD - further improved avionics, airframe and engine, a true killer Flogger even wired for R-73 and R-27
I have little to no knowledge of B/BN/BM or MiG-27's