This all comes from me explaining on IRC that regardless if you think ketchup or catsup is the better spelling, the spelling that makes most sense would be a romanization of the original Cantonese for tomato sauce.

Now, I said that that would be either kezap, kejap, kechap, ketsap or kedsap, but then of course I wasn't able to find support for kedsap and kechap.

So, if you would study Canto at the Chinese University, the romanization would be kezap -- they use a modified Yale romanization, which for this particular word happens to coincide with the Jyutping romanization.

If you were to study Cantonese because you were going to fight the Japanese in WWII and take back Hong Kong, the American military would have used straight Yale, and they would have told you that tomato sauce is kejap.

If you're a person named tomato sauce and you go and register at the persons office, I'm pretty sure they would call you kechap, but I'm so far not able to verify this.

A tomato sauce street in Hong Kong would have Ke Tsap Street on the roadsign.

And "kedsap" is what the road sign standard would be using if it weren't so lossy. The "ts" maps to two phonemes, both unaspirated and aspirated /ts/.