(this is an addition, not a reply - never too sure about forums)
you can extend this technique so you can shift-click all the filtered data in two clicks (say, top left cell to bottom right one). just use existing fields or add them as necessary to sort first (so that your target cells will be contiguous), and then filter on those fields. the sort ensures that all the cells you want lie next to one another, so, when you filter, there are no invisible cells between the ones you can see. just shift click to get 'em all, and paste into a blank table as before.
(a select-all copy won't work because it still returns every bit of data in the table.)