Lack of evidence for symmetric partners and extended spacetime?

Some motivation: It's relatively easy to postulate "supersymmetric theories" - e.g., you can build one by simply monkeying around with the harmonic oscillator H = p2+x2 and linear combinations of x and p using Grassmann numbers - that, AIU, is NOT what one usually refers to as SUSY, but regardless of the specifics, in this simple example I see difficulties in establishing what H is supposed to be, not the least of which is the role the spin-statistics theorem is to play.

Conceptual question (part 1): Regardless; since particles are unitary reps of the Lorentz group, and the SST applies to particle evolution in Minkowski spacetime (let's keep it simple), can't one interpretate SUSY and its extended operator algebra as consequences of particle evolution in some manifold extension M* of spacetime, to which SUSY's "super-Lorentz group" is as the Lorentz group is to Minkowski†?

Illustration-of-concept: For definiteness, let's say M* is complexified Minkowski, and in this theory I have "electrons" propagating along the "real part", and "selectrons" along the "imaginary part", neither necessarily violating SST or anything.

Question proper (part 2): Could this, then, be a natural explanation for the absence of observational evidence on the existence of "spartners"? More generally, I'm also curious about other explanations for this absence, apart from the ol' "build a larger accelerator".

†I don't know if this is how one is to contextualize the super-Poincaré algebra, rather than just god-giving it