One thing you're missing from your current arrangement is a functional dash warning light for your alternator. For that to work, you would need to connect the brown wire from your original harness to the alternator, as described at the beginning of this thread.
My suggestion would be to eliminate your external regulator and its original 4-pin connector, and extend the wires from the original harness over to your passenger-side-mounted alternator. Also, a factory-style alternator connector is available at your local auto parts store. The terminals from your original alternator connector can be popped into this connector housing as well, if you want to reuse your original blue and white wires.
https://www.oreillyauto.com/detail/c...tor/cti0/85841