Thanks, tested this, basically with core64, a 32-bit version of the app runs, but fails when it reaches 4GB of memory. The source compiles and runs on corepure64 in 64-bit mode, but corepure64 is missing many packages.
So it seems:
1) 64-bit apps don't run on the core64 kernel.
2) 32-bit apps don't run on the corepure64 kernel.
I am hoping this info is wrong or something like ia32 is available for tinycore, because the only way forward is an intensive few days of compiling each dependency from source (if all goes well)