No need for excuses,but for interpretations as with the use of acronymes.
Governance of the adverb under VP and Vprime.
Meaning (minimal ambiguity) and style govern the choice.
It is oral/written language, so context and intonation clarifies or modifies interprétation.
It is a to-infinitival Subordonate clause ending the sentence ("assist you further": adv ending sentence sounds heavy and could allow a split interpretation according to intonation)
"I'd be happy to direct you to the bank, to assist you further."
Who is doing the assisting? (ambiguity?)
Fixed VP syntagm?
What about
"I'd be happy to assist you further and direct you to the bank."?
The one uttering is doing the assisting (directing to the bank or else) not the bank
grammatical? acceptable?
"I'd be happy to direct you to the bank to further assist you in the robbery."
This opens another possible position for the adverbe (adding a circonstancial nominal group).
What about "for further assistance" when the speaker is not the one assisting.
"to further assist you" involves the speaker much more and forces reliance on contextual and/or situational information.
"To further assist you, I'd be happy to direct you to the bank"
"I have Diana on the line, and she'll be happy to further assist you."
"I have Diana on the line to further assist you."
(is it to restrain interpretation that "and she'll be happy" was added?): Using 2 coordonate clauses with 2 different verbal main agent ("subject" in certain approaches") does reduce the ambiguity on the main agent of the infitinival clause (here the second pronoun); nevertheless the place of the modifier (here an adverbe) will prompt different possible interpretations out of context (AI has to learn also).
Scenario 1
"I" has to leave work and lets Diane take over the customer
"I have Diana on the line to further assist you."
Scenario 2
"I" doesn't know the answer at one point and Diana is experienced
"I have Diana on the line to assist you further (on the matter)."
"I have Diana on the line for further assistance" to avoid ending the sentence with a modifier that could act on what follows.
In conclusion Not a fixed Verbal Phrase since occurrences of different positioning (of the adverbe) are possible and the governance of the adverb is directly linked to meaning and/or style as well as suprasegmental and extra-grammatical parameters.
NO authority on this matter. Just common use.