To me . . . .Looks like it's just displayed and being all solved for you.
Just stick with the specified low drop out regulator instead of a MORE common 7805, so that you will thereby be able to drain down that 9 V battery to its lowest level while still retaining a regulated output.
Also confirm if that QUITE DESIRABLE - - - MECHANICALLY STABLE, heavy gauge enamelled coil winding is seeming to be ~ 18gauge (or 1 mm to you ).
And, it is being wound on a 1/8 in (or 4 mm to you ) winding form for 10 turns AND should be no closer to each other than is being shown or else, have one coil mounted at a right angle to the other.
? for Audio Guru . . . . is that electret element . . . being a pull from some German equipment, as it doesn't resemble all of the far east counterparts that I have seen.?
73's de Edd