Design idea here: use as much of the 74HCT240 as possible. Hence, one inverter as oscillator, three buffer (I know, this does not really make sense, but wait!) and the block of the other four gates as power amplifier, all four in parallel for use with a step-up transformer. The "PA" is equipped with an enable/disable switch.
So, here is comes, why use three buffers. Well, the first buffer is required since oscillator gate is operated in "linear mode". This first buffer inverts the signal, or in other words, phase-shifts it by 180 degrees. The second buffer inverts the signal again, providing a signal which is phase-shift by another 180 degrees, delivering an in phase signal to the oscillator. Who knows what this can be used for...
OK, now the third buffer seems really useless, but, it is not ;-) This buffer terminated the second one properly, so that always a nice signal can be drawn from either buffer 1 or buffer 2.