GMAT Sentence Correction (SC) | Re: Carnivorous mammals can endure what would otherwise be

"Having" is not the issue in either of the examples you mentioned.

The first is an example of perfect participle: having + past participle: this structure is used to indicate a completed action. The base verb here is "amass", not"have".
Having done my home work, I went to play... correct.


The second example uses "having" directly as a present participle modifier. The base verb is "have". The usage of present participle to refer to a noun touching