comparative adjective + a + noun

There may be differences between speakers or regions. I would not say "I would have preferred more modern a style"; I would instead say "I would have preferred a more modern style."

This is what is called the "big mess construction", which has been discussed on this site before. In my answer to the question “As good a deal as you'll ever get”, I give a quote from and link to one paper on this construction: "The Big Mess Construction", Frank Van Eynde, 2007. In Müller, Stefan (Ed.), Proceedings of the 14th International Conference on Head-Driven Phrase Structure Grammar, Stanford Department of Linguistics and CSLI’s LinGO Lab, 415–433.

Some American English speakers can have "of" before the indefinite article (mentioned on page 3 of "The Big Mess Construction Straightened Out", by Sosei ANIYA), but this is not an essential element, nor is it the origin of this construction. My understanding is that the "of a" variant is infrequent in British English.

how requires this word order

This word order is mandatory in adjectival phrases starting with how: your cited sentence 3, How much longer a journey was it to your old job?, cannot be replaced with *A how much longer journey was it to your old job? or *How much a longer journey was it to your old job?

In the other sentences in your question (1-2), I'm not sure whether it is mandatory.

in general, comparatives allow but do not require this word order

Van Eynde says that in general, comparatives (he only mentions more, but I assume that synthetic and analytic comparatives behave the same way) can be used with either word order:

A further complication is provided by the APs which are introduced by more or less. They can either occur in the canonical position or in the exceptional one (Huddleston and Pullum, 2002, 435).

(6) a. This is a more serious problem than the other.
b. This is more serious a problem than the other

(p. 417)

Although I do feel like the two usages aren't fully interchangeable, I'm not sure what the differences are or how to describe them. Perhaps you (or another user of this site) can look up what Huddleston and Pullum say in The Cambridge Grammar of the English Language to see whether it has more information.

Van Eynde suggests that "a more serious problem" is an "unmarked" usage where more has a negative "MARKING value", while "more serious a problem" is a "marked" usage where more has a positive "MARKING value" (p. 428), but I don't find this terminology/analysis very helpful in terms of figuring out the concrete differences in usage.

a bit longer a wait

I think that It may be a bit longer wait sounds tolerable to me, although It may be a bit longer a wait sounds just as good or better. I'm not sure why the "big mess" word order is used in this context, but I think it's related to the fact that a bit already contains the indefinite article a.

no bigger a house

The use of no is probably relevant, in addition to the use of the comparative adjective bigger. It doesn't sound acceptable to me to use A no bigger before a noun: I wouldn't say *a no bigger house.

Theirs is no bigger a house than ours seems grammatical, but awkwardly formal to me: I believe that to express this idea, I would naturally use an alternative structure like Their house is no bigger than ours rather than this construction.

a = of a

The "a" in those sentences represents how English speakers often contract the "a" that means "of":

a (definition 6 OF 31) preposition 1. pronunciation spelling - a reduced, unstressed form of of : cloth a gold; time a day; kinda; sorta.

and the "a" that is the indefinite article:

a (definition 4 OF 31) indefinite article 1. not any particular or certain one of a class or group : a man; a chemical; a house.

into a single "a" sound.

Therefore,

1. It may be a bit longer a wait. = It may be a bit longer of a wait.

2. Theirs is no bigger a house than ours. = Theirs is no bigger of a house than ours.

3. How much longer a journey was it to your old job? = How much longer of a journey was it...

4. I would have preferred more modern a style. = I would have preferred more modern of a style.

Q & A:

Q: When can I use "comparative adjective + a + noun" and when not?

A: Whenever you can properly say "of a" instead, or if the noun is plural, whenver you can properly say "of" instead. Otherwise, you can't.

Q: When can I add "a + noun" after "comparative adjective" and when not?

A: This is the same question as that above, just reworded. See answer above.

Q: What is the difference between "comparative adjective + a + noun" and "comparative adjective + noun"

A: The former requires "of a" or "of" where "a" appears to convey the same meaning. The latter does not.