Your last reference, p. 358 of Filelfi's Odes
, mentions three other times when Alberti and Filelfo had a chance to renew their friendship, in Florence 1429-1434, Bologna 1437-1438, and Mantua (1459). Bologna is dubious and Mantua too late for Momus, but Florence was certainly likely. Filelfo wrote an ode to Alberti that seems to suggest a friendship, too: Book IV, Ode 6, on pp. 252-259 of the same book. Filelfo seems to have been in Cremona at that time, so probably 1453, on his way to Rome and Naples. I see that the last two pages (of four) of the Ode's English translation are not in Google Books, but the references to Momus are all on p. 255, which is in Google's preview. The notes to the ode are on pp. 416-417, which are also in the preview. Robin, the translator, notes that in the Ode "Filelfo wonders whom Alberti means to satirize in the Momus." Perhaps, but he does not seem to be suggesting that he, Filelfo, is being satirized, and that he is Momus. I can't see that. All he says in the Ode, addressing Alberti, is:
There are some Momuses who say you are writing satires. Surely you are not by chance being criticized for the same thing I am?"
Filelfo had recently published a book of satires himself. Robin's only relevant comment on this passage is "Some contemporaries identified Alberti's architect-god Zeus with Pope Eugenius IV" (p. 416, in Google Books).
In the Ode Filelfo contrasts his own poverty with Alberti's wealth. Describing the accoutrements of wealth, there are some lines that might be critical of Alberti. I don't think so, but I quote them for your perusal, as they are on p. 257, not in the Google Preview:
I've always been eager for wealth follow me as its lord, not for me to follow it. What is mroe riches have brought me neither a mistress, nor fine clothes, nor enticements or dalliances. I indulge neitehr in obscene humor, nor in abundnce of Cyprian wine. And I have no disgraceful amounts of food to satisfy a shameless gullet. Gaming and gambling have taken no pleasure in having come to know my home, nor do silly games of chance live there.
The reason I don't think this is directed at Alberti is that Alberti in his essays shows himself to be no lover of the "Cyprian wine"--i.e. Venus--either. But then again, you never know.
On Filelfo's support by Francesco Sforza, Robin says:
When Francesco Sforza entered the city and was officially consecrated as its fourth duke in March 1450, Filelfo resumed his duties under the new sovereign as court poet and university professor at Pavia (p. xi).
So Francesco seems to have supported him immediately. On the other hand:
But when the wars between Sforza and Venice and their respective allies continued and Filelfo did not receive the stipend he had been promised, he looked to other courts for support.
Perhaps by "fully support" you mean in a way that satisfied Filelfo, or a way that he felt he was promised. That may have been never, since he continues to ask others for money, including Bianca Maria.
I see in the introduction to the translation of Momus
that you linked to, the dates for the dinner pieces" is given as starting in 1430, "which he would go on to augment and embellish over the next two decades" (p. xv, in Google Books preview). Robin wrote a book on Filelfo, Filelfo in Milan: Writings, 1451-1477
, I should probably look at.