When hypercorrection forces an adverb to become an adjective

About a week after I posted this on my blog, a reader informed me that the OED had myriads of examples of 'I feel badly' with presumably the same meaning as 'I feel bad'. The rational part of me could not accept this because as long as 'feel' is used as a copular verb, there is no way an adverb could follow in that manner. It would make nonsense of the sentence. However, 'feel' is an unusual word in that apart from its copulative use, it can also function as an ordinary main verb. Because of the semantic uniqueness of 'feel', might 'I feel badly' be synonymous with 'I have a bad feeling', with 'badly' not functioning as a subject complement, which it cannot under the circumstances? But it still sounded to me as a very odd way of saying it. I was very tempted to dismiss it as a case of hypercorrection that went on to be accepted as correct by reason of its frequency of use.

But as I have always said, English grammar is a little like mathematics in its logic and sensibility. If my speculation that it's a case of hypercorrection is correct, there should be evidence for it. People who hypercorrect an adjective into an adverb probably don't understand grammar in the first place. They can't tell the difference between a linking verb and an ordinary main verb. They will just match a linking verb with an adverb and leave it at that. Over time, lexicographers will have no choice but to reclassify the adverb as an adjective because otherwise, it doesn't make sense if 'feel' remains a linking verb.

If my suggestion that it's a case of hypercorrection is right, at some point in time, the adverb has to be reclassified as an adjective while it still looks in every way like an adverb. And we do have evidence for this. 

In the late 18th century, 'badly' is said to have taken on a new meaning as a predicative adjective which means 'sick, unwell; regretful'. The two examples given by the SOED have linking verbs preceding 'badly' in both cases:

Ay, but she's badly. (D.H. Lawrence) 

Kunta felt badly for having wished sometimes that he might strike the man (Arthur Haley) 

To bolster my argument further, I can think of one more word that again looks every inch the adverb it should be and yet it first took on the role of a predicative adjective, this time, in the mid 18th century - 'poorly' which is defined by the SOED as 'in ill health; unwell'. The only example given in the SOED again has a linking verb preceding it:

They all agreed that he looked poorly. He was pale. (J. Cheever)

What probably started as hypercorrection soon caught on and became standard. Lexicographers having to assign a part of speech to the word had no choice but to call it a predicative adjective. 

EDIT:
Just before posting this article in my blog, I discovered that this idea of hypercorrection is, sadly, not something I can take credit for. An article by Merriam Webster says that the 'common wisdom [for "I feel badly"] is that it's a case of "hypercorrection"'.