Why does the DMM make this circuit "work" ? (Power issues : servo & bluetooth)

so you mean like this ?

No.

Like this:-


The square boxes are the servos.

i can't imagine that's what my DMM was "contributing" ?

Your right it wasn't so that suggests you don't need that much inductance so you only need a small value. That was a general purpose comment for heavy motors.

what sort of inductance/choke levels would be reasonable for 6V spikes of 100mA ?

You can't say without first defining the period of the pulse and you don't know that.

is there a formula for this and what would the 'phenomena' be called

This is called "inductive reactance" Inductive Reactance - Reactance of an Inductor and is the effective resistance an inductor presents when fed with an AC signal. This is a pure inductance where the actual resistance is considered zero.

The formula is inductive reactance in ohms = 2 * Pi * f * L
where f is the frequency in Hz and L is the inductance in Henries