Both of those circuits are for driving tiny ultrasonic transmitters and the first circuit in particular is very inefficient, the second isn't much better. You need to give us some specification for the transducer, is it voltage driven like the one in the circuit, in which case it is probably a ceramic piezo unit or is it current driven like a loudspeaker? The amplifier design can't be decided without knowing what it drives.

There is a lot of overlap in circuits that do the same things while accomplishing different tasks. Radio, Magnetic Induction Heating, Ultrasonics; have a lot of common circuit components. You will need a Frequency Driver, MOSFET Gate Driver, Power Amp, and Speaker.

Piezo might need several hundred volts at low current, dynamic might need low voltage but several Amps. Fs2004 flight1 ground environment pro fullcrackrar 1. You are thinking FAR too small. Even with a 15V supply it would draw around 12 Amps (~35A at 5V), that's twice the absolute maximum for transistors as small as TIP41/TIP42. The transformer appears to be a standard power type for 50Hz/60Hz and there would be zero chance of it working at 20KHz and even less at 80KHz, you would need a custom ferrite transformer to work at those frequencies. I would think in terms of a high current/voltage bridged amplifier feeding a resonant tuned circuit.

If you need 20KHz to 80KHz it would be very difficult to maintain resonance but if you stay at 30KHz it becomes practical. I'm saying the design at the moment might produce 0.1W if you were lucky, just using bigger transistors won't help because you still need more base current than an NE555 can produce. Fitting big tires to a small car doesn't turn it into a racer!

Achieving such a wide frequency range is not easy, the normal method to raise the voltage to 1KV is by using resonant inductive circuits but 'resonant' implies a peak at one frequency, making it tunable would be difficult. You need to reconsider the whole idea and think on a much bigger scale, possibly using several high power (100W+) amplifiers. You will never achieve it using a simple transistor pair. MD1712 - yes, but note that it needs external power drivers.

LM3524 - no, it's a PWM power supply controller. PA98EE - possibly but note it needs 450V supply and the health warning about the substrate material. Even with the PA98EE you still need to more than double the output voltage.

Commercial circuits use resonant circuits, balancing the transducers capacitance with suitable inductors to generate enough voltage but that fixes the frequency so you can't tune it. If you want a broad bandwidth high voltage, high power output you could do it by connecting the transducer across the output of a bridge amplifier. The amp would still have to run from ~500V supply and I would suggest using driver transformers to the gates/bases of the output transistor to provide safety isolation. Driving the amplifiers with one signal inverted would in theory produce 1KV AC over a fairly wide frequency range.