> I grant that Emma may have nodded a greeting to Miss Bates without any evidence but for more than that I need at leat a tiny hint to latch onto.

There is no need for such evidence. A person is not guilty until proven innocent. It's the other way round. The narrator does not suggest in any way that Emma slighted Miss Bates at the Coles' party. There is nothing in the text to support it. It is you who make the claim, and therefore it is you who need textual evidence to support it.

I do not suggest that Emma felt for Jane, merely that she did not wish to speak of the piano-forte. The subject was distressing to Jane; many people-besides Mrs Weston- felt curiosity about it and asked her questions. I am not sure what you mean by "relieve her". Emma refrained from pursuing the subject herself. She did not stop others from talking about it, but blaming her for that is rather far-fetched.

The dialogue from Ch32 is IMO JA's satire, via Emma, towards how people viewed new brides and marriage in general in those days. Emma makes satirical comments, such as "it is encouraging people to marry if you make so much of them" or this dialogue:

-A bride, you know, my dear, is always the first in company, let the others be who they may.

-Well, Papa, if this not encouragement to marry, I do not know what is. And I should never have expected you to be lending your sanction to such vanity baits for poor young ladies.

I always read this as playful wit on Emma's part. She does not mean that people should not pay visits to new brides; she means that making such a big deal of a new wife, making her always the first lady of a company etc works as a vanity bait for women to marry. This dialogue took place after she had already paid her visit to Mrs Elton.

Emma made a point to visit to Mrs Elton in proper time, so I don't see how she is remiss or lets her personal feelings about her cloud her judgement about what ought to be done. In fact, Emma could not have personal feelings of any sort towards Mrs Elton, to whom she had never talked before. The dislike takes place after the visit (as well as a second one). Emma had already done what ought to be done.

Emma does dislike going to the Parsonage:

She could not enter the house again<...> without recollecting. A thousand vexations could recur. Compliments, charades, and horrible blunders..."

and I think she doesn't like Mr Elton at this point either- not to mention the awkardness. So this is a case of her doing her duty despite her personal feelings.