Unfortunately, much like paying cash doesn't save consumers the credit card transaction fee covering markups at most establishments, paying in Bitcoin probably won't either, so this will be in addition to the price he is paying due to credit card fees.I think a gift card is a good solution to this.  I also think that using a theoretical (not yet possible based on all I've read in this thread) sidechain would ultimately use just as much data overhead to send the Bitcoin to the same places unless you actually bought hamburgers in two separate instances at the same establishment before said establishment converted back to Bitcoin.  The only way around that issue is to give someone or something else control of your Bitcoin private key.  We've already discussed the possibility of a trustless system that could resolve that, but even then, it would effectively be a mixer, and potentially regulated accordingly.
ETA: Also, the trustless system presumably has less hashpower, so is less secure.  Moreover, cash would be another good way to work around the hamburger issue, and ATMs are even popping up to deal with this, but I'm assuming you want a sidechain that is effectively denominated in BTC either because you don't want to carry cash, which may allow for the gift card option, or you are imaging a future where fiat isn't a thing, in which case a gift card could be denominated in BTC.Sir, it has been too long since you have watched the Matrix.  Mr Anderson and the sentinels do NOT get along.  That will be three demerits, and your punishment is to get off the Internet and go watch the trilogy (one movie for each demerit).  That should give you time to think about what you've done.