Besides the problem caused by reflections and by the fact that unless you are very close to the transmitter you do not receive a direct wave but one reflected from the ionosphere, there is an additional difficulty.

Antennas with high directivity, which are needed for accurate triangulation, must be very big in the shortwave range (wavelength from 100 meter to 10 meter). Moreover, if they are too big it would be difficult to move them, to be able to measure an angle.

So traditional triangulation is inaccurate in this frequency range.

With modern technologies, using highly accurate synchronized clocks, one could distribute shortwave antennas over a large area, to create a synthetic aperture array, enabling a precise triangulation. However this would be expensive. An amateur would certainly not have such a thing. I doubt that even a state would bother to build such a thing, because it would not be worthwhile.

While precise triangulation of a shortwave transmitter from far away is very difficult, such a transmitter would not be hard to find during a local search wherever it is placed, because there not only the direction, but also the intensity gradient of the signal would allow finding it.