The key to the deductibility of contributions under this program will be the description on the cash register receipt of the purchaser/donor.  As long as it is clear that the extra payment was a charitable contribution to a recognized charity, and the donor has the receipt to show the amount was actually paid, the IRS is likely to accept the evidence.

I don’t know how you would be able to state that a specific person made a gift to you under the program since I doubt that the businesses will identify the donors, especially those who paid for their goods in cash.  Fortunately the donor needs a tax receipt from the charity only for contributions of $250 or more (See Ready Reference Page: “IRS Requires Substantiation of Contributions”), which is 1% of a purchase of $25,000.  Unless you are getting car dealers to participate in your program, it doesn’t seem likely that you will have many purchaser/donors at that level.

I would caution about using a two member LLC as the recipient of the contributions.  Although the IRS has ruled that a gift to a single member LLC owned by a charity is considered a charitable gift to the owning charity (See Nonprofit Issues, 7/16/12.), there is no such guidance for gifts to multiple charitable member LLCs.  You could probably get exempt status for a two member LLC but that would be another step in your process.  If you don’t want to take that step, you might route the contributions through one of the already-recognized charities.