"Переход на Хартли по идее должен дать выигрыш 2 раза" - нет там выигрыша, т.к. и обычным FFT можно получить результат сразу для двух вещественных последовательностей. И вообще:
It was once believed that real-input DFTs could be more efficiently computed by means of the discrete Hartley transform (DHT), but it was subsequently argued that a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs.[23] Bruun's algorithm (above) is another method that was initially proposed to take advantage of real inputs, but it has not proved popular.
https://en.wikiped …Fast_Fourier_transform