A. 5.3 Blessed are the poor in spirit, for theirs is the kingdom of heaven.
B. 5.4 Blessed are those who mourn, for they shall be comforted.
C. 5.5 Blessed are the gentle, for they shall inherit the earth.
D. 5.6 Blessed are those who hunger and thirst for righteousness, for they shall be satisfied.
E. 5.7 Blessed are the merciful, for they shall receive mercy.
F. 5.8 Blessed are the pure in heart, for they shall see God.
G. 5.9 Blessed are the peacemakers, for they shall be called sons of God.
H. 5.10 Blessed are those who have been persecuted for the sake of righteousness, for theirs is the kingdom of heaven.
I. 5.11 Blessed are you when people insult you and persecute you, and falsely say all kinds of evil against you because of Me. 12 Rejoice and be glad, for your reward in heaven is great; for in the same way they persecuted the prophets who were before you.
Thomas
A. 54[.1] Blessed are the poor, for yours is the kingdom of heaven.
I. 68.1 Blessed are you when they hate you and persecute you. 2 But they will not find a place, where they have persecuted you.
H. 69.1 Blessed are those who have been persecuted in their hearts. They are those who have truly known the Father.
D. 69.2 Blessed are those who hunger so that they may fill the belly of the one who desires.
Luke
A. 6.20b Blessed are you who are poor, for yours is the kingdom of God.
D. 6.21 Blessed are you who hunger now, for you shall be satisfied.
B. Blessed are you who weep now, for you shall laugh.
I. 6.22 Blessed are you when men hate you, and ostracize you, and insult you, and scorn your name as evil, for the sake of the Son of Man. 23 Be glad in that day and leap for joy, for behold, your reward is great in heaven. For in the same way their fathers used to treat the prophets.
I have lettered them according to Matthew, since Matthew has all that Luke (and therefore Q, so far as can be known) has, plus extras.
Matthew and Luke switch the order of two of the blessings. Thomas switches the order of three.
Matthew and Luke have contiguous lists of blessings. Thomas does not; they are scattered all over the text.
Matthew and Luke use the blessings as the introduction to a great speech by Jesus. Thomas lacks that kind of structure entirely.
Matthew and Luke begin with the poor, which happens to be the parallel which comes earliest of the four in Thomas. Does that mean something? Were Matthew and Luke influenced to select the first blessing in Thomas to be the first blessing in their speech? No, because Thomas has four other blessings before the one for the poor:
18.3 Blessed is he who stands in the beginning; he will know the end and will not taste death.
19.1 Blessed is he who has come into being before he has come into being.
49.1 Blessed are the solitary and elect, for you will find the kingdom.
So Matthew and Luke selected the fifth blessing in the text of Thomas.
In other words, if Matthew and Luke are drawing from Thomas, they are not independently drawing from Thomas; therefore, Thomas cannot replace Q here (by the definition of Q which I gave from Kloppenborg).
If it happens that either Matthew or Luke is drawing from Thomas, but that the two are not drawing from Thomas independently, then Thomas stands more in the relation of Streeter's M or L than in the relation of Q.