When running lights or headlights are on the transmission shifts too early, causing it to bog down?

I would make sure the ground to the engine block and then to the chassis is good. There needs to be two grounds for the electrical system to work correctly. If this is okay, let's run a test on the alternator to see if it is changing low when the lights are on or if the alternator is throwing AC voltage, this guide can help:

https://www.2carpros.com/articles/how-to-check-a-car-alternator

Please go over this guide and get back to us.

In between when I posted the question and you answered I started replacing the cam synchronizer, so vehicle is non op at the moment. As I mentioned in the question, all grounds have been gone through. In the cab and engine bay. The rear axle has also pooped the bed, so road tests on any fixes will be a no go for a while. My brother had this truck when the problem started, which led to replacing battery, and alternator. So, while I assume they are both okay, once I get it started up, I'll go ahead and do the charging system tests. Any other ideas? I truly appreciate any input on this!

Yep, like I say the battery to body ground is usually the problem but the alternator can cause this as well, when you get it running let me know.