What about using PyVarObject of mp_limb_t and mpn instead of mpz_t? 

Addition:
   - Check signs and allocate.
   - Possibly compare absolute values.
   - Call mpn_(add|sub)_n and possibly mpn_(add|sub)_1 if the integers have different sizes.
   - Overhead for small integers: 1 Python->GMP, 1 if.

Subtraction:
   - Same as addition

Multiplication:
   - Check signs and allocate.
   - Call mpn_mul.
   - Overhead for small integers: 1 Python->GMP, 2 GMP->GMP, 3 if.

Division:
   - Check signs and allocate.
   - Call mpn_div_q.
   - Overhead for small integers: 1 Python->GMP, 1 GMP->GMP, 1 if, maybe a 3 more ifs in mpn_divrem_1.

Pow:
   - Create mpz_t values using MPZ_ROINIT_N(limbs, size) and call mpz_pow(m?). Copy from mpz_limbs_read(result).

* The overhead is after checking if both arguments are integers until going to the right function (mpn_mul -> mpn_mul_n -> mpn_mul_basecase).

Checks for adding integers < 1<<(GMP_NUMB_BITS-1), multiplying < 1<<(GMP_NUMB_BITS/2) and dividing < 1<<GMP_NUMB_BITS can be added.