Reference Request on Preposition Fronting

Currently reading "A Student's Introduction to English Grammar" by Geoffrey K. Pullum and Rodney Huddleston.

Consider the following contrast between the phrasal verbs ask for and come across.

"The information for which I asked."—is given as grammatical.

"The information across which I came."—is given as ungrammatical, as in this case preposition fronting is not allowed.

Are there any good dictionaries which clearly state when preposition fronting is allowed? None of the freely available ones seem to have this feature (Merriam-Webster, Macmillan, Oxfordlearnersdictionaries), not even the web version of the Oxford English Dictionary.

Edit in response to comments: In the example above, 'across' is correctly classified as a preposition. You can see that it can be a complement for a noun phrase in the example: "My travels across the ocean have been perilous."

[1] The information for which I asked.

[2] *The information across which I came.

The ungrammaticality of [2] arises because in the idiom "come across" (meaning "find by chance") the prep "across" is specified by the verb, and thus cannot be separated from it.

We need to distinguish two types of specified preposition, mobile ones like the "for" in [1] and fixed ones like the "across" in [2]. The mobile ones behave in essentially the same way as unspecified prepositions, while the fixed ones do not permit variation in their position relative to the verb.

Another example is the idiom "let off" (meaning "allow not to do"), where again the verb and the prep cannot be separated (we can't say *the work off which I let him). This is a matter of syntax, so I'm not sure if it is covered in detail in any dictionary.

Further, the term 'phrasal verb' is a misnomer. In for example "They fell out" (meaning "quarrelled"), it's just "fell" that is the verb. "Fell out" is not a constituent at word level: it’s a VP. Verb is a word category, like noun, adjective, etc., and it’s "fell" that is a verb: this is the word that takes verbal inflections. So we have [3] but not [4]

[3] They had fallen out.

[4] *They had fall outed.