Good finds. The following is a repost regarding the last of your links of a thought I have to another thread where someone asked how to re-sync the stock TPMS'.
It looks like you could very easily make something similar. The picture of the tool shows it's nothing more than a single wire from the connector to the pistol grip, and then a single wire out to a grounded alligator clip. I'm betting all that is doing is giving you a nice interface to ground out that connector 5 times in 10 seconds.
You could take whatever size female spade connector hooked to a length of wire, connect that to the connector and then leave the other end bare or mate to an alligator clip, male spade, whatever, turn the key on then touch the bare end to a good ground 5 times and bam, same thing done. That "tool" can't be sending any information back to the unit.
This most likely wouldn't work though if you introduced a new TPMS to the setup. You'd need to employ one of the other tools for that.