Look--only one exclusion need apply for the item to be excludable from income. The employee achievement award exclusion does not apply, and for good reason. That provision targets run-rate customary awards for current employees. The word "gift" in the post clearly implicates 102(a), which also uses the word "gift." If 102(a) applies, then the item is excluded. End of story.
The question is whether 102(a) applies. It may. It may not. But more facts are needed to reach an answer. If proper analysis is done, then this issue would be pretty easy to defend on audit. And, given the apparent lack of information reporting (which also supports gift treatment), it's unlikely to arise. (Though the poster should follow the law and not play the audit lottery.)