Like you I have not found any information on the later version.
I will see if I can find some data even a schematic may help.
Yours probably has a output transformer driving the Piezo element. Like mine is.
X10WTI was trying to replace older hard to get parts with surface mounted parts. So you may find a completely different surface mounted controller in yours and powered by around 3 volts. As mine are not current Date Code units.
I have a feeling the Ding Dong tones are generated by the controller chips firmware and not easily modified.
The small power horn SH10A/PSH02 basically looks the same internally. Just responds differently to X10 commands. I did modify one of those to close a small relay when the Security Console sounded an alarm.