Since I don't know the arrangement possibilities of your project, I can't propose a working idea. But I can review the relevant theoretical background.
We can consider as a coaxial Helmoltz coils. In this case the mutual inductance depends not only on the coil length and diameter but also on their relative position, and never forget in calculations that the field direction it is a vector. If L1 and L2 are the self-inductances and Lm is the mutual inductance between coils, the total inductance will be Ltot=L1+L2±2Lm.
the mutual inductance is at maximum when they are also concentrical, i.e. D=0
If the two concentrical coils are rotated, so that their axes are not parallel any more, the mutual inductance decreases, and becomes almost zero at 90°. Continuing the rotation beyond 90° the mutual inductance increases again, but this time with the opposite sign. So, at 180° gives a variation of the total inductance of 4Lm.
If the two coaxial coils are moved along their axis instead, the mutual inductance decreaes and becomes zero at infinity
btw there is in an excellent paper which is dealing in depth with this subject. Feel free to send an email to me.