I'm not sure about that, the soda ash takes part in the chemical process as an electrolyte, TSP is a cleaner - and a good one, but it would have different chemical properties. TSP is readily available at any hardware store or paint supply but it's akaline.
The soda ash is acidic and is listed in those outside web links in this thread as being the preferred cleaner. My point being, other people have gone to some trouble to compile the web postings, if all they had to do was buy some TSP and dump it in, I think they would have mentioned it.
My own mad scientist contraption was sustaining 6 amps. Overnight it dropped to 2 amps. There are several reasons for that I'm sure, but the electrolyte's composition could have been changing too. The acidic mixture may have also been a catalyst in that it enabled the electron transfer but also was consumed in the process as well as the electrical potential of the parts changing over time. Interestingly, changing the fluid bath caused the 2 amp pot to resume at 6 amps. The alkaline bath may work, but not as well. As the original post was baking soda, but cooking off the soda to form a crude soda ash yielded even better results.