what in a name?

Here's another environment where the presence (and the nature) of an adjective influences the projection of a definite article:
The following quotes come from Agnes Grey by Anne Brontë:
p. 165: the charitable Miss Murray
p. 174: poor Mark
p. 186: poor Mark Wood
p. 189 the thoughtless Miss Murray

These are not restrictive modification constructions like:
The little Mary I used to know...

A few more examples:
What did the little Mary say to that? (from Little Women by Louisa May Alcott)

The play began as usual with the little Mary and the little Joseph making their entrance into Bethlehem...

The first apparent generalization would seem to be that adjectives that are acceptable in vocatives (poor, dear) allow the omission of the article. The same is true for French, by the way, where the article is generally obligatory in vocatives.

And here are some examples with the adjective French (normally very strange). Only the first example below is that of genuine non-restrictive modification.
1538 James V of Scotland marries the French Mary of Guise

If I win I am the French Mary Pierce.

The French Mary was very sophisticated, the African one was exuberant, the one from the United States looked like a Borg...

Juliette Binoche, who played the French Mary Poppins

Speaking of French, post-nominal adjectives are totally unacceptable in this construction.
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What have I done to deserve this?

I did a Google search for variants of this construction, and the major observation that I have to offer here confirms my own intuitions: in order to get this kind of an infinitive, some sort of quantification is necessary. As I am not a native English speaker, I would not rely on my own judgments on the topic.
NB: Most examples link back to the pages they come from.

With quantifiers:
What have I done to deserve this?
My daughter did nothing to deserve this.
You've probably done something to deserve this
Has Canada done anything to deserve this?
...the activities for which the nominee is believed to deserve this award...
To deserve this questionable honor, at least one of his ideas had to pass three sequential screening committees.
I thought maybe someday I’d do enough to deserve this...

Without:
*I have hit my sister to deserve this
Or is ungrammatical, after all?
Refuse to satisfy the student’s wants and needs until he/she has worked to deserve this return.

Other quantified elements:
FIFA can be sure that we will work very hard to deserve this magnificent investment in our football
The Emperor must have been an incredibly influential and impressive man to deserve this great protection even when he was dead!

Same as?
other people tell me that I am worthy enough to deserve this recognition
And if I am so wretched a creature as to deserve this fate

Apparent similarities:
What have I moved to get this clause?
I must have moved a CP to get it.
*I have moved X to get a CP.
I must have moved a CP to get it.

What have I moved that I can have a CP?
*I have moved a clause that I can have a CP
*I must have moved a clause that I can have a CP
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The generic predicate?

Apparently, predicates can also be generic:
"So. You're not the complete optician after all. <...>
"I'm not the complete anything," I answered, and I sat up on my blanket. "But how would you know what the complete optician would be like?"
(R.A. MacAvoy, Lens of the World, p. 138)

Confirmation: this type of a predicate can appear with raising verbs:
His brother-in-law, Mr. Hurst, merely looked the gentleman...
(Jane Austen, Pride and Prejudice, p. 11 - 5th paragraph here)

In both cases, the interpretation invokes the stereotype.

Finally, the predicate can be modified by scalarity-sensitive adverbs (which only supports the connection with the stereotype):
He is undoubtedly, a sensible man and in his manners perfectly the gentleman.
(Jane Austen, Sense and Sensibility, p. 288)

Added: Birner and Kaplan discuss this construction in:
2003. Birner, B., and J. Kaplan. Scalar nominals in English. In Proceedings of the 38th Annual Meeting, Chicago Linguistic Society. To appear

They say the effect of using "the" instead of "a" is pejorative.

raising and control; modals

What is the structure of the following example?
Something, however, seemed to him to need doing.
Mary Renault, The Charioteer, p. 12

Is it raising from object to subject?
Something, however, t1 seemed to him t1 to need PROt2 doing t1.
The modal seems to be necessary.
This movie merits watching.
This car requires washing.
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