It's pretty easy to imagine having both 32-bit time_t and 64-bit time_t in a single "executable" as long as the interfaces actually in use between 32-bit-time and 64-bit-time components don't use `time_t` (or derived types).
iow: if the fact that `time_t` is 32-bits is kept entirely internal to some library A used by some library B (by virtue of library A not having any exposed types with time_t that are used by library B, and library A not having any functions that accept time_t or derived types), there's nothing preventing mixing 32-bit-time_t code and 64-bit-time_t code in a single executable/process (in this theoretical case where we use a LFS (ala _FILE_OFFSET_BITS, etc) for time_t).
LFS had/has the same capability for mixing (with off_t being the type in question there).