Are the string buffers always suitably aligned for a int128_t? (You use memcpy in some spots, but casts in others.)
Internally 128bit values are stored on the stack or on the PV slot of an SV allocated with newSV(16). As GCC seems to use 64bit instructions to load 128 bits integers from memory, alignment should be right.
So you say that newSV(16) always allocates the bytes on a 128-bit aligned
No, what I say is that the code generated by GCC uses 64bit operations to move data between the memory and the processor registers so a 128bits alignment is not really required.
Any sane allocator will return memory aligned for 64bits or better. Perl custom allocator (used when set from Configure) guarantees that alignment would be suitable for doubles (so, 64bits)... or at least that's what a comment says in the place where MEM_ALIGNBYTES macro is introduced.
update: Regarding the use of Copy, yes, it is because any string allocated outside the module can be unaligned. That includes SVs using the OOK hack and probably others.