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?