Did you notice that the link to the linguist quotes an Oakland teacher claiming that Ebonics is basically Swahili? That's better, stranger and subtler than it looks

.
Swahili is from the opposite side of Africa to the places where black slaves came from, of course, but Swahili is itself originally a 'pidgin'. It is Arabic mixed with local African languages. It comes from trading; it was the result of Arabs trading with locals just as 'pidgin', a word from a Chinese attempt at the word 'business', itself was. (There is your continuum, NNN

)
As a subject it rather points up the difficulty!
The real difference between 'dialect and 'language', outside linguists' usage, is simply political. Compare: Scots is a dialect, a version , of English spoken in the Lowlands. With modern Scots nationalism some declared it a language. The Scots have a language, Gaelic,but the politicians and nearly everyone else cannot speak or understand it. The Welsh speak Welsh English but don't call that a language. Reason? They have Welsh, a Celtic language, and most either speak or understand it, politicians included, so their nationalism resulted in all road signs and Government documents in both languages and no arguments.
A dialect is only a language when its structure,the grammar and syntax , is different from its ancestor's ,as is the much greater part of the vocabulary. Italian has none of the structure, grammar or syntax, of Latin, nor the vocabulary.
It does not qualify as a separate language from English does it, unless a) its words are not merely English words written as locals pronunce them b) it does not follow the grammar or syntax of English c) a whole book, the Bible or a long novel written in it is not recognisable as English nor comprehensible by English speakers ?
I can write sentences in Norfolk dialect which are incomprehensible to others ( heck, I do that with English

!) but not a text of serious length. Passages from the scriptures written in Geordie or Scots are still recognisable and understood as English yet.
To a degree we have this problem here. It is met by teaching children to write and use standard English. Teachers may even, being local, teach using some dialect .Nobody seeks to outlaw Geordie or Norfolk dialects but then nobody yet has tried to unify Newcastle or the county in East Anglia as a separate race or nation.