Hi,
Hi again,
Thank you again, Clive. My thanks also go to GG.
You said this:
Or perhaps you could use such a word/phrase to start an independent sentence, and see if it sounds OK.
What I am troubled by is the use of word 'independent'. I feel if left alone 'I flunked the test before' would not be truelly independent in that a reader might wonder what 'that' might be in 'the test before that'. I feel that there should be a sentence or two to explain or lay down the context for the use of 'that' in 'the test before THAT' or the second sentence wouldn't be trully independent. When we speak of an independent sentence in terms of grammar, it just means a sentence that follows the rules for forming a sentence, Thus, 'He said it' is an independent sentence.
You are confusing yourself by thinking of an independent sentence in terms of independent meaning. That seems to me to be a philosophical question. It''s like trying to define what we mean by 'an independent thought'. That's a difficult question. 
Also, my other question is in the line of this:
The slanted version of the correct version of my sentence is this:
I excelled in the last test, whereas I flunked the test before that.
To me, I can substitute 'whereas' with 'and' it would work fine.
I excelled in the last test, AND I flunked the test before that. Yes, this is fine, although you have lost the extra meaning, the contrast, that is provided by the word 'whereas'.
But what GG seemed to have said is 'whereas' creates a subordinate clause like 'while': That was my initial thought too, but on reflection it seems similar to 'but'.
I excelled in the last test, WHILE I flunked the test before that. -- Is the use of the comma before 'while' OK? I think it is not necessary. I wouldn't say it's necessary, but I prefer a comma there.
I am confused if 'whereas' is in the same category as 'and' and is able to be called 'a true conjunction -- as called by you' or not in the same conjuntional level as 'and' but in the same subordinate-clause generating conjunction level like 'while'. See my comment above.
Best wishes, Clive