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Sending them home will only be an impact the parents if they care whether or not their children are in school in the first place.

Back in the day (20 years ago) if you owed the school money (usually over-due library books) they would prevent progression to next grade, hold transcripts and/or report cards -- again something like this would only impact parents that cared about the education of their children.

If the school is expecting money from parents for lunches (i.e. the families can afford to pay or are part of a program where they have agreed to pay at least a portion of the expense) then the schools should have the ability to fast track the bill through collection (phone, email notification, good faith efforts to collect before holds on benefits are put in place).

Personally, I never had a problem with the Sun Butter solution, the shame argument is over blown. The kids know which families are poor or struggling and which ones are not, and if there is going to be bullying as a result it will happen regardless of the type of lunch a kid gets.