Variable frequency AC power source
Look around for audio amplifiers in the 2kw / 3kw power region. I think you'll be surprised at the low price (I was).

What is advertised as a 3kW amplifier is usually a 1500w stereo into 4ohm loads that's bridgeable into a mono 8ohm load.

If you do the sums, that's a mono output capable of 150 vrms into 8ohms, as long as you are happy with a floating load, as the outputs are bridged.  If you parallel the two stereo channels, that would drive a ground referenced 2 ohm load with 75vrms, or over 35Arms.

To buy a tranformer, even in the sub-kw range to convert a lower power amplifier's output up to the 100v region, is quite expensive (at least I was surprised by how much they tend to cost). With a transformer, not only do you have a lower frequency limit with voltage (core volt.seconds), but you also have an upper frequency limit with winding capacitance and leakage inductance, and core losses. I can't see a 'mains' transformer getting to 10kHz.

For your voltage, current and frequency requirements, I'd just go for a single commercially available kw audio amp.

WARNING just because it's audio doesn't mean it isn't dangerous. Even a 1kW amp can develop lethal voltages, and fire-starting currents. Take all the precautions with the output of such an amplifier that you would take with mains.