lrdazmmlk, we noticed you struggling with this problem. But I already wrote what I had to say and don't have anything more to say about it. The Arduino Uno can make a frequency of 125 kHz, and that's it.
In my opinion, the rest is not possible with an Arduino Uno, because an interrupt takes 5 µs plus the time for the actual code in the interrupt routine.
For a 125 kHz PWM signal, how many steps do you want ? 256 steps ? Then the base frequency is 32 MHz (or 64 MHz, I'm not sure). That is also not possible with an Arduino Uno.
Trying to create such a signal with direct register writing will have too many jitter which is not good to detect the modulation. Even if you can make such a signal, then I don't see how that will help because the detection is a problem.
Is the 2 kHz modulation a PWM modulation ?
The most reliable way is to solve this in hardware. For example a PLL of 125 kHz, then you have the 2 kHz modulation signal.