Some comments on your 2nd proposal:

1/ In "Install Transifex Client", you mention an alternative, consisting on
downloading PO files for each resource.

Even it that's possible, it implies to then combine individuals PO into one
single PO file. Not so easy, so you should rather not mention that alternative.

2/ You can build fdrpg first, and then update translations. So I think that it
could be simpler to explain how to build the game (by referring the dedicated
web page), and then explain how to update a translation:
  cd po/
  make tx-pull
  make update-gmo

This can be done each time a new translation is to be tested...