"Why she did not like Jane Fairfax might be a difficult question to answer;"

And then;
"her conscience could not quite acquit her."

The use of the word 'quite' means - she's not completely able to acquit herself - but to some extent she can. She's not completely drowning in her envy of Jane's playing.

Following are quotes of your 'opinion'.
>resents Jane for being so "perfect" and accomplished,

Accomplished in music, yes, but "perfect"?
Show me a quote where it says Jane is 'perfect' and that's what Emma resents.

>brilliant pianist with beautiful handwriting

Beautiful handwriting is the praise from an aunt. We have Mr Woodhouse praising Emma's beautiful handwriting, on the puzzle;

"..fondly pointing out, as he took up any stray letter near him, how beautifully Emma had written it."

>who is so very good to her aunt and grandmother

For a few weeks every year? While Emma is good to her father all the time.

>and so polite and well-spoken

Apart from Box Hill is there any quote in the book telling us Emma isn't but Jane is?

>and pretty and ... etc.

We know Emma is very pretty, even beautiful (according to Mrs Weston and Mr Knightley).

In addition, Emma doesn't care about how she looks.

"I love to look at her; and I will add this praise, that I do not think her personally vain. Considering how very handsome she is, she appears to be little occupied with it;"

In the end I have one question;
According to you she's just one big bundle of jealousy in just about everything as you have listed, with nothing to redeem her.
What is she actually proud, and vain about? ;-)