Are there any card abstractions / bucketing methods available online that can take a hand on the flop, turn and river and spit out an "equivalence" group. (Almost like a lookup - for implementing in code)

Such that AJ on K73r is roughly equivalent to AQ on K72r to shrink the game tree.

The average and variance hand rank of AJK73 on the river is similar to the avarage and variance hand rank of AQK72 on the river.

Not sure what you mean. I thought most abstractions used E(HS) and E(HS^2) to categorise hands?

E(HS) and E(HS^2) will group too many very different hands together in this scenario
Hand rank is a number that erm... ranks a hand. Royal Straight Flush is top rank
Average and variance arise from rolling out all future cards to river.

I see, so E(HS) is not a great method. I suppose the publications that I read that used it were 10 years old.

How would hand rank be better though? There is no "flush draw" rank for example because it's not related to showdown.

What do you mean by averaging and variance? We enumerate all possible cards and see how our hand rank changes?

I didn't say that. Ehs isn't good for the application you describe. If you think it is why don't you use it?

Find all possible rivers that can develop from the hand.
Find the hand rank of each one
Find the average and variance of the list of hand ranks

I think you have understood the idea now. So you can answer your latest questions yourself with some experiments.

Yes

... Are these available anywhere or just your own private work?

Although, honestly, I'm sick of looking at code. I'd rather someone had summarised the theory behind these things in such a way that would make it NOT appropriate for academic work.

If it was easy and publicly available, there would be no money to be made from it