But to think of it as "on both sides of the verb" is not the best way to understand it.
It is not that the speeches are reproduced regularly AND that the speeches are reproduced verbatim, rather it is that the speeches
are ( regularly (reproduced verbatim) )
regularly modifies "reproduced verbatim" not merely "reproduced".
The phrase are reproduced expresses what happens to the speeches via the agency of an implicit, unspecified agent. Let's recast as active voice. This would be grammatical but would sound a little wooden:
The state-run papers regularly reproduce verbatim the
This is far more likely in speech:
The state-run papers regularly reproduce the
president's speeches verbatim.
In the active voice version, the complement verbatim naturally follows the object, president's speeches.
In the passive voice version (are reproduced) the complement verbatim naturally follows the past participle.
It is so with any adjunct of manner:
Around here, we often make chili with lots of cayenne pepper.
Around here, chili is often made with lots of cayenne pepper.