If my opponent triggers The Painted Table and I have a Naval Escort in play, can I choose to kneel 0 Warships to pay the cost for Naval Escort and immediately get the effect cancelled, or do I have to kneel at least 1 because it's a cost?

You cannot define X as 0 for Naval Escort because you cannot successfully kneel 0 Warships or successfully choose 0 target characters.

It has long been established that if you choose to kneel a character that is already kneeling, a character does not kneel successfully (meaning that you do not, among other things, create an "after a character kneels" Response opportunity). So in order to successfully kneel the Warship , a location needs to change status from "standing" to "kneeling." Similarly, choosing 0 characters does not successfully make anything the target of the effect.

If you cannot pay the cost of an effect successfully, or choose all required characters successfully, you cannot successfully initiate the effect. So you cannot define X on Naval Escort as "0" just to say that you (successfully) triggered a location.

Thought as much, thanks.