Contributors to the discussion of this question have pointed out that to need is a stative verb, one that expresses a state of lacking rather than some action. The present tense "I need" is an enduring present: I have discovered something I lack, I don't have it now, and the remedy is some ways into the future. This would seem to cover the time period of the progressive "I am needing", making that verb form unnecessary and perhaps unidiomatic.
I propose the hypothesis that the progressive "I am needing" is an idiomatic way of expressing urgency, carrying the aspect of the speaker being impelled to fill the need. It is accompanied by a narrative using present participles (in progressive verb tenses or present participles) to express the currency of the situation.
As evidence, I offer texts from the book-google, as mediated by the Ngram viewer. From the religious fervor of the story in Sunshine to the political maneuvering of Conor O'Brien to various pressing errands, they mostly offer stressful situations in the present tense, speaking of the time current to the narrative and requiring quick acton. (The exception is from the novel Lake Country, marked below with an *, "She is as willing to talk as I am needing to talk", which I think this is stylistic choice to make the verb forms equivalent.)
I don't find the same situation for the past progressive. More typical is this passage from The Strand Magazine from 1913:
I got up and lit my pipe, for I was needing a smoke. I heard a snore. I looked around. Tom was asleep again.
This seems less urgent, and the rest of the narrative is not couched in the past progressive as
I got up and lit my pipe, for I was needing a smoke. Having heard a snore, I looked around to find that Tom was sleeping again.
I offer the following caveats:
I have not included all the matches. I left out false drops (along the lines of "I got up at 3 am needing to pee" or "Here I am, needing a drink"), narratives reporting the speech of non-native speakers of English, and matches that didn't give me enough context.
Google books is an imperfect tool as it may not be representative.
I may be guilty of selection bias for a pet idea.
I've weighted the dice a bit in my favor, as I claim the conditions are sufficient but not necessary.
"Father, ... I have been thinking of going with John to church
"Then I'll go too," was the prompt reply,....
The eldest girl, who had been listening on the stair to what was passing, now came into the room,...."But, mother," cried the girl, bursting into years, "you must not go without me, for I am needing to be saved too."
Sunshine (1873), W M Whittemore, ed.
Q: You have the privilege of having the 640 acres?
A: Yes, sir.
Q: Twenty-five acres of it is all you can use in cultivation?
A: That is all I am needing to use.
Records and Briefs in Cases Decided by the Supreme Court of Minnesota (1902)
"Straight or crooked [votes]?"
"You may search me. But knowing Tom Gryson a little, I should put my money on the marked card."
"Naturally," said Blount dryly. "Still, I am needing to be shown.
The Honorable Senator Sage-brush (1913), Francis Lynd
I am trying to help my son write a book of his 7 1/2 months in Chile and Argentina, and I am needing to "soak up" atmosphere, descriptions, etc., from various sources to couple with his stories, his journal, etc.
Biennial Report -- Oregon State Library (1940)
I need it urgently, because it contains my only copy of my 'Notes on the Making of a Poem', and I am needing to quote something in my Preface for the American edition of my Selected Poems. I am having, at the moment, hell with the American Anthologies....
Selected Letters 1919-1964, Dame Edith Sitwell
I am completing a thesis on the subject of "expressive intonation" and am needing to get frequency read-outs of recorded solo instrumental performances (especially of Pablo Casals, etc). I am looking for someone who has a working device or program which can do this.
The Music Researcher's Exchange -- Volume 6 (1978)
*Inside a very nice lady who looks like Dolly Parton welcomes me to sit next to her at the bar. She is as willing to talk as I am needing to talk....
Lake Country (1994), Kathleen Stocking
From his [Patrick Hilllery, Minister for Foreign Affairs] earlier discussion with Sean Lemass he fully realised the danger of taking the Northern Ireland problem to the UN. As he put it himself later, "Here I am needing to make a speech and yet trying to avoid a vote."
To laugh or to weep -- a biography of Connor Cruise O'Brien (1994), A J Jordan
My area in southern Illinois for the second time now in the last 4 years has just undergone flooding. The SBA was magnificent, working with FEMA in the approach to helping our small business that just literally were wiped out wit those floods.
I am needing to understand, because we were able to get emergency declarations and so on and get assistance in very quickly, working with Mr. Witt and with the SBA,....
Massachusetts' Request for Disaster Funds from the SBA (1996), United States Congress, House of Representatives, Committee on Small Business, Subcommittee on Government Operations
Because of my amniocentesis, I know that I am giving birth to a daughter. I wonder whether there is something I am needing to digest with regard to being a daughter, something that must be processed from my daughterhood in order that I may
Mother Mysteries (1997), M T Hansen
... I, in sceptical fashion, remain equally absorbed by my cultural assumptions. The result is that with her I am often in my "comparative-studies mode" and if I am needing to return to my silence, we end up by merely exchanging cliches.
Holding the silences: a Nepal notebook (1998), P Eckersley
I didn't like the thought of leaving him on his own. But who knows what fate lies in store.... Everything happens for a reason, says my mother, and this is probably just the kick in the pants I am needing to set me on a new vision quest.
A Celtic Childhood (2000), Bill Watkins