The Desire to Give:
The Medrash says (Shemos Rabbah 51:2) that Moshe went to Betzalel and saw that the Mishkan had been completed and some materials remained. He said, “Hashem, we made the Mishkan and are left with some leftovers. What should we do with the materials that remain?” Hashem told him, “Go and make from them a ‘Mishkan Ha’eidus.’”
Rav Bunim of Peshischa zy”a explains that there are some people who give away all they can but still have a burning desire to give more. However, there is nothing left for them to give, just like the Mishkan, which was completed but there was still more to give. The desire to give more is very beloved to Hashem, even more than what one actually gave. Thus, Hashem said to make “from them” a Mishkan Ha’eidus – meaning that the people with a desire themselves become akin to a Mishkan.
This is the meaning of the words “habocher b’shirei zimrah” – He chooses the remainder of the song. He loves those who remain with songs and praises that they desire to say even after they have praised Him as much as they can.