Ummmm, Huifeng, you just proved my point -- this passage comes from the 內藏百寶經, i.e. the ārya-lokānusamānāvatāra-nāma-mahāyāna-sūtra or the 'phags pa 'jig rten gyi rjes su 'thun par 'jug pa zhes bya ba theg pa chen po'i mdo.
By the time of your sources, it has got "mahāyāna" in the title, but not at first.
It's probably been co-opted by the mahāyāna after the fact.
Using later Sanskrit names is not going to show what it was originally recognized as.
Looks to me like Lokakṣema was primarily involved in translating Mahāyāna sūtras. My objection still stands.
Verses from it exist in the Prasannapāda(as well as Mahāvastu) but that merely shows that it may have reworked some earlier material
It was first translated into Tibetan in 8th century.
The bold part above, "shows that it may have reworked some earlier material" is important, and I totally agree.
This is one reason why there are some texts which are not easily categorized as simply Mahayana or not Mahayana.
My own take is that some of these texts were originally from various schools, such as the Mahasamghikas,
from where they circulated to some degree, and that perhaps only later did they get the Mahayana reworking.
That reworking often included a change of title. Looking at different versions, over time, we can see the changes.
Another good example may be the Salistamba. While some scholars see it as Mahayana, the earlier versions
were not considered as such, and were just basic texts of the Mahasamghika or some other early school.
The end of the Skt version we have states: "āryaśālistambaṃ nāma mahāyānasūtraṃ..."
But this is not found there in the Chinese versions from many centuries earlier at all.
Some of the Chinese texts later have the "Mahayana" in the title, but no other indications that it is.