It depends on the architecture of your software. If the AGPL-licensed package is just used in an back-end application on a server, and not exposed to 3rd party interaction (through a proxy or not does not matter), then this back-end application can be considered as 'internal use' and you will not have to provide the source code. You mentioned 'internal use only' but it is unclear from your description which criterion you chose to determine that. If the AGPL-licensed package is running on the frontend of a customer-facing server, then you would be required to provide the source code.
It depends also on the legal structure of your 'agencies'. If the agencies are wholy-owned subsidiaries of the insurance, then the interaction of their PCs with the server-application can be considered internal use, and thus you won't have to provide the source code. That is true even if consumers, who come to the agency's office, interact with the agency's PC to for example sign a form. It would be different, however, if the agencies are not owned by the insurance, independent legal entities, in this case, if the AGPL-licensed app is running on the frontend of a server and the agency is interacting with that, then you would have to provide the source code to them.
I assume your insurance has a law department. They will anyhow want to know if you are using strong-copyleft software. Consult them. And consult your company's OSS Policy.
W.r.t. the question if AGPL requires the delivery of source code to the users (especially company-internal users), 2 things have to be considered.
a) The Preamble of AGPL v3.0 emphasizes the word ‘public’ in the sentence “Therefore, public use of a modified version, on a publicly accessible server, gives the public access to the source code of the modified version.” I believe that the intention is that running AGPL-licensed software on a company intranet should have the same effect as running the same software on an employee’s computer. And there it would clearly be considered as ‘Internal Distribution’.
b) The other item is that §13 only refers to ‘modified versions’. If the AGPL-licensed software runs without modifications (and without combining/linking it with other code) there is no need to offer the source code.