The following modules had to be installed manually before the server would run:

Catalyst::Runtime
Catalyst::Plugin::AutoRestart
Test::Warn
Test::Most
Test::Aggregate
REST::Utils
Object::InsideOut
Math::Random::MT::Auto
Data::UUID::MT
JSON::Any
Net::CoverArtArchive
SOAP::Lite
Function::Parameters
DateTime::Format::ICal

Once these modules are installed manually, carton install --deployment successfully verifies all modules in the deployment.