What is simpliest possible guitar active preamp design
Instead of using a split battery, I think a virtual ground at 1/2 the supply would be better.  That way you are essentially running from a single power supply.  That leaves the possibility open, for example, of using a boost converter to make reasonable voltage, and doesn't end up with two batteries that are used somewhat separately.

A TL072 is not appropriate for &plusmn;3.6 V.  It's not even specified for 7.2 V operation.  Take a look at the headroom it needs, both for input and output, with &plusmn;12V supply.  Or, put another way, 7.2 V is inappropriate for a TL70x.

In your circuit, C1 actually hurts.  There is no need to AC couple, and C1 leaves the positive input floating DC-wise.

With a virtual ground, you would AC couple both the input and the output, but that would be a different circuit.