I believe that the first published reference for Meeks was actually for a coffin. There is also a record for a broadside they published that mentioned all kinds of furniture, but I'm not sure that it included pictures.
The fact is, whether your table is Empire or Empire Revival, a positive attribution is extremely difficult without a label of some sort. You could say "attributed to" but your table type is common enough that coming up with a definite "Meeks trait" is very unlikely in a sea of other manufacturers.
The problem is compounded by the fact that there are no monographs on Meeks and that much of the firm's work has until recently been confused with that of John Henry Belter, with whom J and J Meeks were contemporary.