So many reports on the Internet assume that the baptism of desire is visible- 3

Agreed.We are clear in our proclamation of extra ecclesiam nulla salus.
However there are so many reports on the internet which do not make the visible - invisible distinction.
Then even among supporters of the SSPX and the St.Benedict Center it is an either this or that.
There is a baptism of desire or there is no baptism of desire for them, with reference to extra ecclesiam nulla salus.
It is not there is a baptism of desire (invisible) and also the need for all, with no exceptions, to be baptised with water (visible).

The visible/invisible distinction that you make is fine, as long as you acknowledge the possibility that everyone in Paradise, without any exceptions whatsoever, may have the character of sacramental Baptism in Water, at least after the Law of Baptism was promulgated if such, indeed, is the will of the omnipotent One and Triune God.

In any case, BoD/BoB has absolutely no impact whatsoever on our proclamation of EENS and that's what is important.