First of all:
You've said that D.Miguel had to renounce in favour of D.Duarte Nuno because of the Saxony incident.
Which was never prooved as Wikipedia recognizes.
The Saxony incident happened in 1900, and D.Duarte Nuno was born in 1907.
As to D.Francisco, all I read about his eventual homossexuality was in Wikipedia.
Which press mentioned the incident ? Why on earth would he be in London for Edward VII's coronation as the obvious invited would be his Bragança-Saxe-Coburg cousins ?
If he really was homossexual, despite the scandal that fact ment in the early 20th century, that was not cause for his being outranked from the succession line. - Read the commentaries from the Legitimists about him, further down.
Many kings and princes were homossexual: Ludwig II of Bavaria comes to mind. As well as Ferdinand of Bulgaria.
Kaiser Willelm II was very near those "circles", The duke of Clarence, and so many other minor royals.
At the time there was not such gutter-press as today where a homossexual king or crown prince would be crucified despite that comes into the "political incorrectness".
From Malcolm Howe "The Braganza Story"
" Prince Francisco José fought with the Austrian troops and died in 1919 from pneumonia (I guess that soon enough Wikipedia will say it was from AIDS) on the isle of Ischia, near Naples, whilst still a prisonner of war, captured by the Italians"
(Wonder if the Duke of Porto, living also in Naples, ever met his prisonner cousin)
"He, of all the descendants of D.Miguel I, most resembled his grand-father, the King, in his physicall appearance and had also inherited the musical talents of the Braganzas.
His mother had died when he was two years old, and he was brought up by his aunt Infanta D. Maria Anna, before his father married again.
When in 1893 she married the Hereditary Grand-Duke of Luxembourg, Francisco José, at the age of 13, composed the nuptial march for the wedding.
The family always called by the portuguese diminutive of his name "Chico".
He was the joy of their home and became an indefatigable traveller.
His communicative kindness and effusive happiness made the Legitimists regard him as the most esteemed of their Princes, with all the qualities and defects of the Portuguese race.
He supposrted his brother at his wedding in 1909 and they were together in Galizia offering their swords to Paiva Couceiro to fight in both the 1911 and 1912 incursions."
D.Franscisco was also a bullfights aficionado and he was himself a bullfighter.