Bex...
I shall dig out some references for you, cant grasp them off the top of my head. But bearing in mind that Radar Control is useful for class A crossings, most CAS upward of 195/245 is class C.
You are absolutely correct with the MATZ being class G, and likewise that SVFR clearances are not required in class D; SVFR clearances are constantly being interrogated, when actually they are only really useful in low class A (eg. London).
But as I say, BZN/LYE class D is essentially established for the type of ac they operate, applying CAS rules allows the controller a little more SA of the area to provide a safe transit. Quite rightly I cannot think of a useful reason for SVFR for D but they do somehow :-/. As for the type of service, they can only provide the usual LARS ATSOCAS (BS, TS, DS).
SL