I am not sure its this straight forward as presented.
1) this table has to be a known name on the page (probably means by name....not sheet.1)
2) sure you can use props, but you would need to define all the props names ahead of time so the drop can find its entry
(imagine 2 squares to be dropped, Square 1 looks for props <square 1>....square 2 looks for props <square 2>
There is no shapesheet function to add a row in the shapesheet....so the props section needs to be fully articulated.
3)you cant do this as a shape on the page since the shape name is variable and there is no such thing as 1 shape
discovering another shape dynamically without VBA
(back in 2003, visio guides called out that the shape name (e.g. sheet.2468) can change do to shapes added and deleted.)
4)probably want to look at the setexpreat*** functions so that if you update the shape, the changes are pushed back to the
page props.
5) if there is plans for more than a few shapes, you probably want to do this in VBA (or even python).
6) you may be able to leverage the document stencil to trick/spoof the behavior you want.