This is the complete shloka:
व्यासाय विष्णुरूपाय व्यासरूपाय विष्णवे।
नमो वै ब्रह्मनिधये वासिष्ठाय नमो नम:।।
The English translation would be something as below:
Vyasa is the form of Vishnu or Vishnu is Vyasa, I bow down to the such descendant of Vishishtha Muni.
Vasishtha's son was Shakti; Parashar was son of Shakti, and Parashar's son is Krishna Dvyapana hence he is referred as descendant of Vishishtha Muni.
This implies that this shloka is for Krishna Dvyapana (28th Vyasa) and not for all the Vyasas in general.
And many Puranas (one reference is already mentioned in your question) mention Krishna Dvyapana (28th Vyasa) as Vishnu avtar so there should be no doubt in this.
As mentioned in What were the previous births of the characters of Mahabharata?
Aswatthaman was born on earth, of the united portions of Mahadeva, Yama, Kama, and Krodha
[Update as asked in comments]
In Vishnu Purana: Part3: Chapter 3, Brahma, Manu, Yama, Surya and Indra etc. have been mentioned as previous Vyasas but still they have been mentioned as portion of Vishnu.
And reason for this is given in the same chapter. This is because in Vishnu Puran (or in Vaishnavism), Vishnu is the Supreme Brahman and
He (Vishnu) is the soul of all embodied spirits.
This world is Vishńu; it is in Vishńu; it is from Vishńu.
By this logic, all are portion of Vishnu. And if Yama can be considered as portion of Vishnu then, Aswatthaman who is portion of Yama (and Mahadeva, Kama, and Krodha) can also be considered as portion of Vishnu even before he becomes Vyasa.
