Thanks for sending the picture. Those sure look like D. lotus to me. I'd bet money on it. Your taste description matches the lotus I've tasted at the US Germplasm Repository at Davis, CA.
D. Lotus is used for rootstock in warmer regions, your tree may have been grafted then the graft failed. Here in Indiana my lotus persimmon seedlings freeze to the ground every winter then spring back up the following summer. Kaki the same.