Yes that "moving the voicebox up" trick is more of less the goal of many of the fast track tutorials I have seen, back when I needed it the only one I found was Melanie Ann Philipps descriptions. I did that as well and it worked for me rather ok for a while, I still do that, it has become rahter normal for me although I slip sometimes when surprised. I think it is not enough though, at least for me. I still have a low pitch and that gets me in trouble. In the beginning Imanaged to raise pitch a bit and that was good for a while but I guess mostly the pitch but maybe also the voice box thing lead me to get long term trouble with my voice. It was getting rough and eventually I could not keep the pitch. I read in an article by a voice surgeon that almost all of his patients who had been post of 10+ years had some nodules or whatever on their vocal cords that made them sound less than optimal. Can be cured it seems by not raising pitch too much and by some other training.
Another thing that is lacking when using only that trick is obviously to get a proper alternative resonance and loudness/projection. I still have that problem now as I never learned it another way and I was just always the one with the weaker voice. Its not that much of an issue as there are plenty of women who also tend to speak very low volume, so it does not come over as unusual I think, but its better to fix that, I suppose.
Still would like to know how to use the other features in praat except the pitch. I noticed that if I make the same pitched sound with or without chest resonance, I get very different readings in praat. Just adding chest resonance drops the Hz number by like 40 or 60 Hz it seems. The added low frequencies from that resonance are probably entering the calculation. So I am not sure how reliable that pitch detection is...
