It would depend on where your temporal focus would be. as influenced by Colin Fine's answer here:
"I had finished the work on friday" / "I have finished the work".
with the present perfect your focus is on the PRESENT moment:
I was happy to have finished everything early
It means an action that has been completed but with no specification as to when or if it ended.
When you use the past perfect:
I was happy to had finished everything early,
It is describing a time in the past, the distant past but it does not influence the present or future - the action is completed.
Take this example:
Present perfect: The kids have eaten dinner.
[They ate dinner at point A, it is point C now. Note: For the present perfect, point B does not need to exist. A and C are the only points that matter.]
Past perfect: The kids had eaten dinner before the nanny went home.
[The kids ate dinner at point A, the nanny went home at point B, it is point C now.]
The difference is that in the present perfect example, the result of A is that the kids do not need to eat now, at point C, but in the past perfect example, the result of A is that at point B, no one needed to prepare dinner for the kids.
One of the rules of the perfect infinitive - to have finished - is that it can refer to something that will be completed at a point in the future:
We hope to have finished the building by the end of March.
But this is going beyond the timeline of your context, because the question of finishing is not in debate, like in the above i.e when the building will be completed, but rather in your context which is used depends on what temporal point you wish to emphasise - it's a nuance or a slight difference in semantics. It is even more confusing because 'to have finished' is also used to refer to events that will happen at a later date in the future, not simply ones that have already been completed.