How can I register a new passport for my DTV visa while being outside Thailand?

If only this question was asked 4 times weekly

you make a copy of the data page and the last entry/exit stamp on the DTV of the old passport (the one the DTV was issued under)

Put it with the copy you already have of the PDF print out you got from the thai consulate (that IS your visa) and show those copies with the new passport when you stamp in.

They will note you got the DTV issued on an earlier passport and stamp you in for 180 days on the new one when you arrive.

That's it, you show those copies when you stamp in to thailand for the duration of the DTV

You can't. Bring an old passport with you when entering