Here's my native speaker's take on which sound natural and which don't:
1a: Talented as he is, he is not yet ready to turn professional. [Natural.]
1b: Talented though he is, he is not yet ready to turn professional. [Natural.]
2a: Try as he might, he couldn't open the door. [Natural.]
2b: Try though he might, he couldn't open the door. [Unnatural.]
3a: Lazy a boy as he is, he kindly helps others. [Unnatural, possibly ungrammatical. I changed the part after the comma to be grammatical; I assume that's not what you're asking about.]
3b: Lazy a boy though he is, he kindly helps others. [Unnatural, possibly ungrammatical.]
4a: Oldest in our workshop as he is, he works hardest. [Unnatural.]
4b: Oldest in our workshop though he is, he works hardest. [Unnatural.]
Below are some speculations about what's going on.
The words as and though appear in various familiar phrases, or phrase templates. The opening clauses in the sentences above echo them more or less strongly, contributing to their perception as natural, unnatural, grammatical, and ungrammatical. First I'll list all the familiar phrases that I see being echoed, and then I'll explain how they accord or clash with the sentences above.
(A) X as he is can be understood as a short form of As x as he is when x is a quality that comes in degrees.
(B) Trait as he is can be understood as Trait, as he is, or as an inversion of As he is trait, when trait is a quality that you either do or don't have. In other words, this reading is the same as Since he is trait.
(C) Trait though he is can be understood as an inversion of Though he is trait, where trait is a quality that you either do or don't have.
(D) Verb as he might can be understood as Try as he might try or As he might try, that is: in whatever manner he might try.
(E) Try as he might is itself a stock phrase.
(F) Verb though he might can be understood as an inversion of Though he might verb. This means that you're thinking of verb as something you do or don't do, not as something that you can do in a variety of manners.
How well the sentences accord with the phrases they echo
(1) You can understand talented as either a quality that comes in degrees or a trait that you do or don't have, so (1a) accords with both (A) and (B). There is some contradiction between (A) and (B), but I think ordinarily a listener doesn't notice and just rides along to the clause after the comma. (1b) matches (C), so it's easy to hear that way, but talented is mainly a quality that comes in degrees, so (1b) is just a little off.
(2a) is a perfect match with the stock phrase (E), so it gets a free pass. There's no bending or varying going on. (2b) seems to echo (F), but if you take couldn't as past tense, then it doesn't make sense: "Though he might try, he was not able to open the door." However, couldn't is pretty flexible with regard to time, so there are reasonable interpretations: "Though he might try, he won't be able to open the door." Because (2b) uses the word try, though, it seems to clash with (E). (E) is a strong attractor, so failing to match it can feel like a grammatical error even if technically it isn't.
(3a) echoes (A) too weakly to be easily understood as "As lazy a boy as he is"; "lazy a boy" doesn't fit x in the formula, though you could hear it that way. Maybe you could understand it through (B), "As [since] he is a lazy boy", but I think it's very hard to hear it that way. You could understand (3b) grammatically through (C), as a scrambled version of "Though he is a lazy boy," which is that sentence's only claim to grammaticality. The most obvious unscrambling comes out as "Though he is lazy a boy," which doesn't make sense.
(4a) echoes (B) and (4b) echoes (C) pretty clearly, since oldest is a superlative and doesn't come in degrees. I feel a little disoriented, though, because in an unscrambled version you'd precede oldest with the: "As he is the oldest in our workshop" or "Though he is the oldest in our workshop". It's okay to drop the article in the unscrambled versions, and certainly the scrambled versions cannot take an article, so the result is a feeling of clumsiness and a suspicion of ungrammaticality.