I could be wrong, but I think Republic in the Caymans is specifically for international banking and might be more easy-going than in Guyana. It might be that they focus on wealth management and want some six or seven figure deposit, though.
Scotiabank might be another option. Approach locally and abroad, see if you can leverage a local connection in TT to open an account elsewhere. Things︀ like that used to be easy across the Caribbean but it's getting harder and harder︁ with increased KYC and derisking.