Why not just look into the obvious, as in what significance the number 3 has in OT theology? A lot of straining at gnats going on here ...
"Three
Three signifies completeness and stability, as represented by the three Patriarchs and the three pilgrimage festivals –Passover, Shavuot, and Sukkot (I Kings 17:21; Daniel 6:10).
3+1
This is a number cluster that signals the fulfillment of God’s plans (Amos 1; Daniel 7:25)."
Judaism and Numbers | My Jewish Learning
.... and as applied to the NT and the neo -Jewish theology, best answer is ...
"The number three symbolizes a harmony that includes and synthesizes two opposites. The unity symbolized by the number three isn’t accomplished by getting rid of number two, the entity that caused the discord, and reverting to the unity symbolized by number one. Rather, three merges the two to create a new entity, one that harmoniously includes both opposites. On its own, Entity A leaves no room for Entity B, and Entity B does not allow for the existence of Entity A. Entity C demonstrates how A and B really are compatible, and even complementary. Bringing together two opposites (A and B) requires the introduction of an entity or common goal (C) that is greater than both of them."
On the Meaning of Three
It should be easy enough to get the allegory re life, death, and rebirth, the Trinity, etc., from the above, as well as the links back to the OT and Torah, as represented by Jesus's ministry of '3 years' and other symbolic references, following the Torah pattern and seeking a return to the dynamism of Moses and the Laws, and much more, in a single reference without interrupting the flow of the main narrative of Mathew's chapter with a lot of confusing divergences into a multitude of issues, which could all be cross-referenced and pondered at later convenience. Filling in One and Two is also easy in the context of Mathew as well.
A couple more examples of significance of the number 3:
Meaning of the Number 3 in the Bible
"The Meaning of Numbers: The Number 3
The number 3 is used 467 times in the Bible. It pictures completeness, though to a lesser degree than 7. The meaning of this number derives from the fact that it is the first of four spiritually perfect numerals (the others being 7, 10 and 12). The 3 righteous patriarchs before the flood were Abel, Enoch and Noah. After the deluge there was the righteous "fathers" Abraham, Isaac and Jacob (later renamed Israel).
There are 27 books in the New Testament, which is 3x3x3, or completeness to the third power.
Jesus prayed three times in the Garden of Gethsemane before His arrest. He was placed on the cross at the 3rd hour of the day (9 a.m.) and died at the 9th hour (3 p.m.). There were 3 hours of darkness that covered the land while Jesus was suffering on the cross from the 6th hour to the 9th hour. Three is the number of resurrection. Christ was dead for three full days and three full nights, a total of 72 hours, before being resurrected on Saturday, April 8, just before sunset.
Appearances of the number three
There were only three individuals who witnessed Jesus' transfiguration on Mount Hermon. Those who saw Jesus' glory on the mount were John, Peter and James.
The apostle Paul was an exceptionally well educated person. In three different occasions he quotes directly from Greek poets (Acts 17:28, 1Corinthians 15:33 and Titus 1:12). He also was privileged to visit the location of God's throne, which is in the third heaven (2Corinthians 12:2 - 4)."
... and more at the link. A little research can find much more implied in the number 3. Numerology is a big deal in biblical literature and theological references, yet it seems most ignore it entirely for some bizarre reason.