I do not have a source, but I think I have a strong answer that would be acceptable based on the Torah the OP is examining.
1) The Torah only mentions the reward of long life by two mitzvos.
a) Honoring parents. "Honor your father and your mother as the Lord your God commanded you, in order that your days be lengthened,..." (Devarim 5:16)
b) Sending away the mother bird. "You shall send away the mother, and [then] you may take the young for yourself, in order that it should be good for you, and you should lengthen your days." (Devarim 22:7)
2) The mitzvah of making a fence around your roof results in credit for saving other lives. (It also seems to be the only mitzvah that says so specifically.)
"When you build a new house, you shall make a guard rail for your roof, so that you shall not cause blood [to be spilled] in your house, when the one who falls should fall from it [the roof]." (Devarim 22:8)
Since the mitzvah of "sending the mother", results in the lengthening of one's own life, then because of the principle of "מצווה גוררת מצווה, one mitzvah leads to another mitzvah (Avos 4:2)" ; it makes sense that it should lead to the mitzvah of building a fence for your roof, which will save other lives as well.
Now if you will ask why the Torah didn't use "honoring parents" as the example which leads to "building a fence"; we can answer two ways.
a) Rashi to Dev. 22:7 explains that this commandment (sending away the mother bird) is very easy to fulfill (as opposed to honoring parents) and yet it still leads to the reward of building a new house with its mitzvah (roof fence). The Torah wanted to teach that easier mitzvos grant great rewards and therefore how much more so do harder mitzvos. So the Torah preferred the example of sending the mother bird.
b) The Riva on the Torah, comments "למען יאריכון ימיך. ולהלן בשלוח הקן אמר והארכת ימים לו' לך אם תקיים מצות כבוד אב ואם הם יתפללו עליך שיאריכון ימיך כי יאריכון ימיך בא מבנין הפעיל היוצא באחרים"
He explains that the promise of a long life for honoring parents is a result of the parents praying on your behalf. However, the promise of long life for sending the mother is a direct result of the mitzvah itself. (He learns this from the different grammar used in the promise by honoring parents which suggests the lengthening of days will be accomplished for the person; by others.)
If so, then the Torah would choose "sending the mother" as its example over "honoring parents" because long life as a theme is a direct result of the mitzvah of the mother bird (and seems essential to it), where it is indirect by the mitzvah of honoring parents (The parents pray on your behalf, since you honored them.)
(It is still possible according to the Riva that even if your parents do not pray for you, Hashem would still also grant you longer life; but the grant of long life by the mother bird is certainly more of an absolute which is not dependent on others at all.)
3) Now since one needed to make a fence for the next mitzvah, then the rule of "מצווה גוררת מצווה, one mitzvah leads to another mitzvah", should create a reality where the person needs to get credit for building more fences.
When one plants a vineyard and is worried about Kilayim (forbidden mixtures of different plants) the best way to make sure one section of the vineyard is not mixing with other crops, is to make a fence. (fences and other barriers are used in some cases, to separate otherwise forbidden plantings in Mishnayos Kilayim, ex. Mishnah 4:3)
4) If someone prevents the mixing of forbidden plant species, then they merit to be able to prevent other illegal mixtures such as preventing (the next level above plants) different animals from working together when the Torah forbids it.
5) If someone prevents plants and animals from mixing in a forbidden manner then they merit to protect the next level (humans) from violating wearing a mixture of plant and animal products. (things which came from both plants and animals: wool from sheep, and linen from flax.)
As we now see, each mitzvah and its specifically chosen resulting mitzvah, illustrates the principle of "מצווה גוררת מצווה, one mitzvah leads to another mitzvah" in fine detail. We also see why the mitzvah of sending the mother bird is the only choice which matches well with the mitzvah of making a fence for your roof.
I hope this helps.