> series them in this fashion
No. As drawn, when you are not connected to any primary tap on T2, the secondary of T2 is "dead" and high-Z, so output will be very poor.
Also the marked impedances are all wrong, but that's probably unimportant.
Are you adding this in front of a diff-input amp? Then use one 600/150:600/150 transformer with all windings in series as an auto-transformer. If the whole string goes to the mike-amp, then you can get voltage ratios of 1:4, 1:2, 3:4 (1:1.33), and 1:1. Impedance ratios about 1:16, 1:4, 1:2, and 1:1. If the load is a typical 2K mike input, then the mike sees 125, 500, 1K, and 2K ohms. If the mike is 125Ω, then the actual change of signal level over the whole range of taps is not quite 6dB.
More complex affairs are possible.