How can I then tell avr-gcc that all registers but "r0" are clobbered?
In particular how do I tell it that X,Y,Z are clobbered?

For any register other than Y, __tmp_reg__ and __zero_reg_, add respective registers to the clobber list. For example, in order to clobber r30, you would

___asm ("..." ::: "r30");
// or
___asm ("..." ::: "30");

For the ramaining registers:

• Clobbering Y may not be possible when it is used as frame pointer.
• Clobbering __tmp_reg__ and __zero_reg_ (R16, R17 on AVRrc; R0, R1 on all the other AVRs) has no effect since they are fixed registers (not allocated or handled by GCC's register allocator).
  For example, when your asm is clobbering __zero_reg__ by means of a MUL instruction, you have to clr __zero_reg__ at the end of the asm template since otherwise, the following code will malfunction since avr-gcc expects __zero_reg__ to always contain 0.