What best describes the sort of father St. Joseph was?

Question

St. Joseph was a father to Jesus (Luke 2:48: "… Behold thy father (πατήρ) and I have sought thee sorrowing."), having all the rights a father has over his son, but he was not the natural father of Jesus; all Jesus's flesh came from the blood of His mother, Mary. Nor was he a "foster father", as he didn't adopt his Son from another marriage; Jesus came from within Sts. Mary's and Joseph's true marriage.

Thus, what best describes the sort of father St. Joseph was?

Answer 1

The phrase Nutritor Domini is another term used to describe St. Joseph. Foster Father maybe leaves a little too much to the imagination as a Foster Father or Guardian might not be considered as nurturing as a biological father, but owing to what we know about St. Joseph from scripture, he wasn't afraid to take Mary into his home and raise Jesus as his own (once prompted). So there's no reason to suspect he wasn't 100% fatherly in his vocation.

Answer 2

Boniface Llamera, O.P., Saint Joseph, p. 77:

Virginal father […] [is] true and, without doubt, the most sublime and exact of all the titles which have been given the holy Patriarch.

and

St. Pius X approved and indulgenced the ejaculation: “O Joseph, virginal father of Jesus!”⁷⁴

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_{74. ASS 40 (1906), 59.}

Cf.

• Gabriel Breynat, O.M.I. and François Blanchin, O.M.I. "Saint Joseph, Père Vierge de Jesus." Revue de l'Université d'Ottawa, 1938 1936, 73-80, 149-58, 81-111.
• Garrigou-Lagrange, Reginaldus. "De Paternitate Sancti Ioseph." Angelicum 22, no. 3/4 (1945): 105--15.