So yes, that date is only an upper bound. But there's a reason the scholars in this area believe what they do regarding the origins. For the type of cultural contact that can lead to the adoption of a writing system, that kind of closeness is important. You can't just handwave away a gap of several actual human generations, while at the same time ignoring the other major powers that are much closer and certainly exerting stronger cultural pressure than Carthage.
There would have been a lot of refugees from the Punic disasters, and staying a long way from Roman centers would favor survival.
Being the only literate group in a wide area would explain the surrounding majority's adoption of a non-standard script, otherwise a mystery. Use of the script could be confined to ephemera indefinitely long before a change that led to its use to inscribe durable material, so a gap, while inconvenient for historians, is hardly disposative.
To directly rebut, rather than appealing to authority: The oldest attestation of Elder Futhark currently at 160 CE. So your proposal has Phoenecian developing directly into Eldar Futhark 300 years after Phonecian was no longer attested. And even then, Phonecian use had been reduced to Carthage while having developed into other systems elsewhere. Note that Gothic origins were ruled out for a mere 100 year difference, so this seems like quite the gap to cover.