Is there a way to noun a prepositional verb phrase?

I'm not precisely sure how to ask this. I can turn certain verb phrases into nouns, and they sound good. The major reason to do this would be facetiousness but the grammatical aspect intrigues me. Some examples:

I like to hit home runs. -> I like home-run-hitting.

I often attack bears. -> I often go bear-attacking.

However, with prepositional verb phrases, it doesn't seem to work out.

I enjoy standing on desks. -> I enjoy on-desk-standing*.

He's good at taking care of things. -> He's good at of-things-taking-care*.

He is known to rely upon God. -> He is known for his upon-God-relying.

Are the first two productions correct, and if so, what's the technical term for them? And, is there any way to get a correct result for the latter three productions and others like them?

Nominalisation is a noun phrase generated from another word class, usually a verb.

Here's the Cambridge Dictionaries Online definition, which also specifically mentions that the process can be used to form noun phrases (as opposed to the simplest case, which simply involves using a verb as a noun - for example a big spend).

OP's examples also feature...

inversion - any of several grammatical constructions where two expressions switch their canonical order of appearance.

(i.e. the "normal" sequence for his upon-God-relying would be his relying/reliance upon God).