I am not aware of any such organisation.
The FAR (the US regs) has very specific strictures about such things e.g. charity flight etc. one has to have logged several hundred hours before it is legit, notify the district office and a whole lot more.
When I get home I will post the reference to the FAR - there is likely and even more onerous EASA version - I know of this as I was asked to do the very thing here at the airport open day a few years ago, looked up the rules and I didn't make the minimum hours, plus the hassle of the district office approval was just too much.
No matter what happens with a simple PPL if you are not paying the full cost of operating the airplane you will be breaking the law and potentially exposing yourself to civil liability if something goes wrong.
What you need to do post PPL is build the minimum hours for a commercial license and then maybe such a wheeze would work.