auxiliary do-support: do murder

This is not do-support per-se. This sentence is not interrogative or nugatory in nature, and do is coming after the subject pronoun he, so there is no subject/verb inversion. The reason it is coming near the middle of the sentence is because of fronting, which reorganizes some elements of a sentence to change its focus.

Did is instead being used as a marker of the emphatic mood. According to the Farlex book of Grammar's Mood section:

The “emphatic mood” refers to the use of the auxiliary verb do to add emphasis to a verb that would otherwise not require an auxiliary.

We usually use emphatic do to stress the fact that something is the case. For example:
“Yes, I do know that we are meeting your parents tonight.”
“Well, she does have a Ph.D., after all.”

We can also use do to add emphasis to demands or requests, as in:

“Do be careful, John.”
“Oh, do be quiet!” However, the use of do in such imperative sentences is now rather formal and old fashioned.

In this case it seems to be emphasizing that the fact did happen, which is common in legal contexts.