Hey @traveladdict, I am the founder of a non-profit myself and since it is about feeding the hungry I have had some experience with restaurant owners and chefs (we are a fairly new non-profit so I have limited experience)

1) Restaurant owners as a whole are charitable and willing to help,  but they have the causes that they support.  Many restaurant give portions on there intake to a certain charity and I think would welcome a way that would make it known what charity they support and possibly allow there dinners to contribute as well.  But your system would need to be targeted to the specific charities the restaurant owner likes.

2)  Even though the above is true, there is a fine line to pressuring the dinner to give something.  If you are wanting to add anything to there check were the dinner just fills in a donation amount, or have donation envelopes on the table or something, this is going to be a hard sell.  Even if you don’t see it as a hard sell it will be.
 
3)  Know exactly what you are asking for and ask it.  Like said above there needs to be a benefit (how is it going to benefit the restaurant).  That is why the grouping and what not work, they sell the restaurant on the benefit.  If you can’t bring more people into the restaurant, or somehow show that with your system people enjoy their experience more than without the system than you have a hard sell.  Unless you can do number 1 and pitch it to a charity the restaurant owner already really cares about and want to support
 
I think we are thinking about doing something that may be similar to what you are doing specific to out organization though.  It might be a good idea to actually approach different charities and have them push it to the organizations that support them, perhaps if you can make the system a little less specific to restaurant the charities can individually push it to any retail/restaurant type business.