As promised. Bonus content: intro also rewritten for Hannibal. Since Phoenician has gendered second person pronouns, the lines assume the addressee is male. Some lines received only minor adjustments, while others were rewritten considerably to be more idiomatic. I have also revised all of my original transliterations now that I can actually read Hebrew script and have a better idea of what Reckoner wrote.
Fixed Transliteration: ʾanūk Dīdō, hammalkot u-haʾum leQart-ḥadaš. Maqademe šum lekoʾn bišum qīn banay Kᵉnaʿan.
Rewritten: ʾanūk Dīdō, milkot weʾam leQart-ḥadašt. ʾibirrek lekom leBaʿl weleʿaštart beʿabūr bnē Kᵉnaʿn.
"I am Dido, queen and mother of Carthage. I greet you in the name of Baal and of Ashtart on behalf of the Canaanites (lit., 'sons of Canaan')."
NOTES: Tyro-Sidonian Phoenician made little use of the definite article so I removed them. Vowels adjusted to accord with Phoenician sound laws. The expression BRK le-DN is widely attested in Phoenician to mean "greet in the name of DN." šum is an Aramaicism in Talmudic Hebrew that has no place here.
Rewritten: ʾanīki Ḥannībaʿl, roʾš wešupṭ leQart-ḥadašt. ʾibirrek lekom leMilqart weleTinnit beʿabūr bnē Kᵉnaʿn.
"I am Hannibal, general and suffet of Carthage. I greet you in the name of Melqart and of Tinnit on behalf of the Canaanites (lit., 'sons of Canaan')."
NOTES: Punic seems to have developed a different first person pronoun from Phoenician (see Poenulus). Melqart and Tannit replace Baal (Haddad) and Ashtart as the chief gods of Carthage. The Carthaginians still called themselves "Canaanites" as late as the fifth century (see Augustine).
Fixed Transliteration: Yabōʾ ʿōšer lemaqōmkom...Harahōqīm miššapat hayyom.
Rewritten: Yiṣleḥ Baʿl ʿal qarūtka--ʾak, qarūtka ʾīš bešade miyyam.
"May Baal prosper your cities--namely, your cities that are inland from the sea."
NOTES: I rewrote this one pretty extensively to sound less Hebrew and more Phoenician. The formula ṢLḤ-DN for "may DN prosper you" is characteristic of Phoenician. The usage of šade, "field," to mean "inland" is typical Phoenician but not Hebrew.
Fixed Transliteration: Ḥopṣēnū lā laʾarṣ - hū lekom - mēhayyom u-šapatū hū leʿammēnū.
Rewritten: Bal ḥapaṣnu leʾarṣ -- hū lekom. ʾips yam wešapt ʾīš leʿammēnu.
"We do not delight in the land -- that is for you. But the sea and the shore is to our people."
NOTES: The negative lā is completely unattested in Phoenician or Punic; bal is the correct negative particle. The first phrase is the same elements as the original but adjusted to be more correct in Phoenician. Second phrase is identical. Third phrase is more strongly adjusted to accord with Phoenician idioms. The original was probably more or less acceptable (with sound adjustments), but I feel my rewrite is more idiomatic and less Hebrew.
Fixed Transliteration: (Sigh) ʿatto malḥoma bitabkēnū. Habbiṭū bayyom - ʿatto haʾup maleʾ beʾoniyyatay.
Rewritten: (sigh) Hen, ʾiʾgud-na lekom milḥomat. Ḥazē beyam - gam ʾup maleʾ beʾoniyyatay.
"Behold, now I will wage war upon you. Look to the sea -- already the horizon is filled with my ships."
NOTES: Hebrew prefers hinne; Phoenician prefers hen. Several things here may be perfectly grammatical in the original, but they're not expressions I'm familiar with in Phoenician so I changed them. ḤZY is a verb that means something very different in Hebrew, but in Phoenician it means, "look, behold, gaze upon." ʾoniyyat is not attested in Phoenician, but there's no reason to assume it's not the word for ship.
Fixed Tranlsiteration: Malḥoma? Hakkesilem ʾantum? Maqōmkom yidaʿū ḥurb kiʾEpirus Sagunt.
Rewritten: Milḥomat? Nabol ʾatta? Qarūtka yidʿū ḥilq keʾEpirus wekeSagunt.
"War? Are you a fool? Your cities will know the lot of Epirus and of Saguntum."
NOTES: Kesil is a Hebrew word for both fool and giant (and the constellation Orion). Its equivalent kisl probably means the same in Phoenician, but I opted for nabol, which is actually attested in Phoenician. I again substituted qart for maqōm just to be more Phoenician. I believe the original was meant to read "your cities will know our sword (sic)..." but I opted for "fate" per the English translation. The failure of the original to repeat the preposition ke- is ungrammatical, at least in Biblical Hebrew and Phoenician.
Fixed Transliteration: ʾal titgaʾawū bine šᵉḥaqōm. Bayyūm ʾaḥad tiraʾū maqōmkom hakkol baʾeš.
Rewrite: Bal titgeʾewūn bešeḥaqēm. Beyūm ʾeḥḥad tiraʾūn roʾška kul beʾiš.
"Do not glory in the heavens. One day, you may see your capital all in flame."
NOTES: I had to trust Reckoner's idiom as it's not attested in Phoenician; however, the vocalization is surely wrong and should be more analogous to Hebrew's. ʾal is only used for non-indicative verbs; should be bal. Made a minor correction to the conjugation of the verb in the second phrase and replaced "place" with "head (city)," again eliminating definite articles.
Fixed Transliteration: ʾanūk danā ʾet kil mī lō yōten ʾet ḥayyū leššum Qart-ḥadaš.
Rewritten: ʾanūk ʾeqab ʾet kul mī ʾal yuten ʾet ḥayyo ʾet panē Qart-ḥadašt.
"I curse anyone who would not give his life for (lit., 'to the eyes of') Carthage."
NOTE: QBB is a uniquely Phoenician form so I couldn't resist using it, especially since it much more closely captures the original meaning than DN. The accusative particle ʾet isn't used much in Phoenician except for emphasis, but that makes it appropriate here. Once again, lō is never used in Phoenician and šum is a Talmudic Aramaicism.