All I managed to do was write one tiny little accessor method for Game::Matrix. Sigh.
The reason for this is that when I carefully read the process of calculating a value in the next schema, most of them will be based on a formula that requires either mangling the matrix more or else setting up another item in my object hash. I've elected, for the sake of clarity, to do the latter. As such, I wrote the getting method that snags that value, and rewrote the init so that it included setting that value.
Although, now that I think of it -- since that value's going to get set once every iteration, I really should have a _set_denom method and just call that...sigh.