My first recommendation would be to take a careful look at, and do a thorough review of, those existing programs that already affect food prices in this country, some of which have their genesis in historical concerns that go back the better part of a century and do not in any way reflect our current public health concerns. Some of those could be reformed or reformulated in ways that would address those tensions.
Looking at tensions within the tax policy as well, the current tax policy is a good idea; however, when you try to start drawing a lot of bright lines around certain food items, there are the problems I mentioned about targeting and substitutions, and there's also just the administrative complexity of it. A system that might be taxing a large number of food items differentially from others would be very difficult to administer, both for government agencies and for the retailers involved, and that cost should not be ignored.
Finally, looking at trade policies and the like, while keeping an eye out for the effect of those on public health, we must also keep in mind that public health concerns pursued in other countries have sometimes run afoul of trade regulations. An example rather recently is a tax the Mexican government tried to implement on high-fructose corn syrup beverages; it was seen as a technical barrier to trade and was struck down. The United States complained about it because they are a major exporter of high-fructose corn syrup to Mexico. We need to keep in mind that we also have various treaties in place that might also restrict our ability to do some of the things we've been talking about today.