After an hour or so of scouring the the fig database, and remembering the 5 or so type of figs that Whole Foods was selling last year, I have come to 100% conclusion that I have a Celeste fig tree rather then an LSU Purple fig tree.
I am really disappointed since I have been looking for almost a year to try and locate a true LSU Improved Celeste fig tree, to avoid the issue of dropping fruit. I bought the "faux LSU Purple" from WF b/c it was such a nice shaped tree and
after reading a bit about the LSU Purple, I didn't think $20 was too much to spend for a 2-3 year tree. So now I have the tree I was trying to avoid, go figure.
The pictures of the figs from my tree and the F4F database are almost identical, as are the leaves. The dropping only helps to confirm the truth. This tree is the only tree on my deck out of 6 currently fruiting tree to be dropping its fruit.
The figs for sale last year were Celeste, LSU Purple, Black Spanish, and Hardy Chicago.
In the end, both Kane and I got something different then we thought by buying figs through WF.
So my search continues. If anyone has a rooted LSU Improved Celeste they are willing to sell, please let me know. Thanks to everyone who helped me identify that my LSU Pruple was a true LSU Purple.