Adverbs + Present Perfect

Solution 1:

Adverb placement is not fixed, and as with other elements, I think most of it depends on what you want to express.

"He has always been an academic and a charitable person". This is a kind assessment of a man, and also the simplest and most common construction.

"He always has been an academic and a charitable person.* This is more emphatic, as if in defense of some alternate version of his history.

"He has been a wise and, always, a charitable person." This emphasizes the constancy of the latter attribute. All are "correct".

"We had been slowly drifting down the river when a bear attacked." is no different really than "We had been drifting slowly down the river when a bear attacked." To my ear (AmE), the latter sounds a bit more common. I agree it would be unusual to break up had been in this case, but "he had often been seen..." is not an unusual construction.

"He had been either sick or exhausted." is much the same as "He had either been sick or exhausted." Here, either is emphasized because of it's less common placement. Both are grammatically correct.

Solution 2:

I'd probably prefer

'We had been drifting slowly down the river ...' .

Adverb placement is flexible but sometimes quirky.

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An emphasiser (adverb of degree - or arguably pragmatic marker) would sometimes be placed after the (first) auxiliary:

"I have really been trying so hard." (same usage as 'I've really tried this term.')

Notice that the modal pragmatic marker usage of really would be placed differently:

"I really have been trying so hard." (here, really = honestly / believe me) OR "I have been trying so hard. Really / Honestly!"

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'Either __ or __' is a correlative conjunction. Strictly, it should join grammatical equivalents:

"Either he had been sick or he had been exhausted."

"He had either been sick or been exhausted."

"He had been either sick or exhausted."

However, ellipses can lead to other variants, and if they sound reasonable they often catch on. Hopefully, the ellipsis will not generate an ambiguity.