I'm having trouble picturing your design. Can you post a photo?

In general, you need to protect against movement a) when it occurs against something that does not move similarly, and b) where there are distances perpendicular to the grain (wood won't expand much along the grain, only across it).

An example of a) would be long grain lying atop a crosswise frame member, and a (counter) example of b) would be long grain lying atop a longwise frame member.

If the grain in your table top is oriented to the long dimension of your table, you can secure the top along one side (screw up into the bottom of the table, use a cleat, etc) and then use something like your Z clip along the other side.

But I gather from your question that you are aware of this and don't have great access. Photo? Drawing? Please?

In general, you need to protect against movement a) when it occurs against something that does not move similarly, and b) where there are distances perpendicular to the grain (wood won't expand much along the grain, only across it).

An example of a) would be long grain lying atop a crosswise frame member, and a (counter) example of b) would be long grain lying atop a longwise frame member.

If the grain in your table top is oriented to the long dimension of your table, you can secure the top along one side (screw up into the bottom of the table, use a cleat, etc) and then use something like your Z clip along the other side.