Matthew, I don't understand your definition of maps in your category are. You say \$$\mathcal{X}(a,b) \leq_{\mathcal{X}} \mathcal{X}(c,d) \$$ but I don't know what \$$\leq_{\mathcal{X}}\$$ means.

My gut is saying that you should fix \$$\mathcal{V}\$$ and then look at the enriched categories for that \$$\mathcal{V}\$$ rather than sticking together all the enriched categories for all \$$\mathcal{V}\$$.

Anyway, it might be worth you going back a step. What structure does what you call 'a monoidal preorder over a discrete poset' have? What is another name for a monoidal preorder over a discrete poset?

Can you give an example of such a thing?

Can you give an example of an enriched category over such a thing?