After posting this question, I found that in Toras Moshe HaShalem ad. loc. they explain that he's referring to Rav Menachem Azariah MiPano. He says this idea in his Asarah Ma'amaros Eim Kol Chai 1:7.
They also cite that the Chasam Sofer cites this elsewhere in his Chasam Sofer Al HaTorah to Genesis 32:5.
Another question one may have, is according to the baal shem tov's explanation on that part of davening, that "tamid", constantly, renews the work of creation, is that everything is being created constantly from nothing, not only every day (at the beginning of the day), as is the simple inference from that tefilah
Another point, for example, is the ...
The standard approach is to Daven for him as (name) ben (father's name) based on the Maharshal, although there are other customs.
See here and here for example.
See also Yechaveh Da'as 6:60 for more on praying for a non-Jewish parent.
Wishing him a speedy refuah sheleimah and may you all share many more years of excellent health.