So I upgraded and now have a Mavericks test system, and got the command line build working on there after some tinkering. Apple only includes clang in their latest command line tools, so gcc and llvm-gcc are merely symlinks to clang, which is a confusing hack. More relevant is that as of Mavericks, clang uses libc++ as the default C++ library, before it was always libstdc++. It's likely that some libraries (e.g. Boost) are detecting that change and configuring to use libc++ and possibly C++11, which causes errors later in the game build.
One workaround is to use clang explicitly instead of "gcc", and tell clang to use libstdc++ via flags (-stdlib=libstdc++). That seems best for backward compatibility, clang actually gives an error if a deployment target < 10.7 is used with -stdlib=libc++. I think for this to work properly in Xcode as well, Premake will need to be modified to add those flags and use clang instead of gcc on OS X. clang is available even back to Xcode 3.x on Snow Leopard, so I'm not worried about losing compatibility there.
Another problem is that even with the above workaround, I was unable to build with a target < 10.7, since SDL fails to build when using some formerly deprecated functions and types (distinct from the errors mentioned and fixed previously). I don't really care to fix SDL's OS X SDK compatibility at the moment, so instead I will look into the best way to support 10.5-10.9 with our release bundles if possible.