I reached out to Sail Caribbean Divers who said that they could obtain the temporary 30 day license. I specifically inquired about the requirement for the immigration stamp. Their response is below but it seems that for the temporary license you don't need the immigration stamp.

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"They only require this if you request the actual permit. For me to process them I receive a permit number which allows you to fish.
Any further action would be directly from the fisheries department and then they require your proof of entry."

Regards,

Kina
Sail Caribbean Divers
(284) 541 3483