Multiple Tone outputs with 16-bit timers

Hi All,
I have an interesting application that I'd like to use the Tone library for (if possible). I've had difficulty researching a solution, so I'm posting my problem here. This is for the Arduino Mega.

Fundamental problem...

I need three independent 50% duty cycle frequency outputs. Tone seems like a nice fit for this.

Each output needs to be programmable between 1Hz to 5KHz. I understand that 16 bit timers are required for the lower frequency range and have only been successful in getting one 16-bit Tone working (timer 1). This worked well. I understand that timers 3-6 on the Mega are also 16 bit. Is it possible to set and use Tone with two additional 16-bit timers.

Any guidance would be appreciated - even if it's to advise that it's not feasible. In which case, I'd shift to using PWM outs sourcing external timer circuits (not as ideal of course).

Thanks,
Greg