In order to sidestep this debate, I will use Chinese characters instead of contested historical names throughout this post.
No texts in the 渤海 language survive, so all we can do is speculate based on historical sources. In fact, it appears that the 渤海 may have used the Chinese language as their literary language, based on a passage from the history of the Jurchen Jīn dynasty:
乙未，诏百官诰命，女直、契丹、汉人各用本字，渤海同汉人。Ethnically, the Jurchens seem to have believed that they were related to the 渤海, since the Taizu of the Jīn dynasty promulgated an edict saying:
On the yiwei day, [the emperor] issued edicts to the hundreds of officials. For the Jurchens, Khitans and Chinese, he used their own scripts; For the 渤海, [he used] the same as the Chinese.
女直、渤海本同一家。Indeed, the history of the Jurchen Jīn says:
The Jurchens and 渤海 are originally one family.
The 粟末靺鞨 allied themselves to 高麗, and took the surname Dashi. After [the Tang official named] Li Ji destroyed 高麗, the 粟末靺鞨 guarded over Dongmo Hill. Later, they became the 渤海, were called kings, and for ten generations had writing, laws, music, official courts, systems, customs, five capitals, fifteen prefectures, and sixty-two districts.The 粟末靺鞨 here are one of the seven tribes of 靺鞨 from whom the Jurchens held themselves to be descended. The characters 粟末 are reconstructed as *sok-mat in OCM (Minimal Old Chinese), and represent an ancient name for the Sunggari river (now called Songhua). I expect the river name was something like *sugmar, which became *sumgar through metathesis, *sunggar through assimilation.
If we assume that the collective name of the seven tribes, 靺鞨, was pronounced the same as the phonetics 末曷, then that gives is an OCM reconstruction of *mat-gât. The Early Middle Chinese reconstruction of 渤海, for comparison, is *bət-xəy'. It seems like it is not entirely impossible to say that the name 渤海, which appeared in the Táng, is a later form of the older 靺鞨, having undergone some sound changes. The sound change from m > b is not well represented, though we do find it in the Manchu words for "monkey", monio and bonio.
The language of 渤海, if it was anything other than pre-Jurchen, should have left some loan words in Manchu. Indeed, the Manchu language has a large store of enigmatic words whose etymologies can't be found in Tungusic, Mongolic or Chinese. Much of these will no doubt be Khitan, but some of them may be 渤海. Khitan itself is likely to have some 渤海 loans, as well.
Someone really needs to do a careful archeology of Manchu in order to make sense of the enigmatic vocabulary. Among the words whose origins are indeterminate are many words containing palatal velars (represented by -giy-, -kiy-, -hiy- in the Manchu script), including the name of the Manchu royal clan, gioro. The following relatively common words are also enigmatic: boigon, "family"; boo, "house"; bonio, "monkey"; abka, "heaven"; aga, "rain"; wece-, "to shamanize"; ganio, "supernatural".
Someone also needs to do an analysis of the pre-Chinese place names of the Changbaishan, among which there are a fair number with palatal velars. I wonder if a careful linguistic archeology might not reveal the presence of an otherwise unattested substratum language in the area of the Yalu river and Changbaishan.