I agree with you that the evening congestion is likely what's tanking your speeds. As for fiber, my state received federal funds to bring fiber to all the areas that have no terrestrial internet access. It is a SLOW process. They've been working on it in my area for at least 3 years now. The only thing left is for the fiber company to dig the micro-trenches that will bring the fiber to the homes, and then do the connections. I contacted the provider to ask when they were expecting to actually do all this, and they said it would take until the end of 2025. The original estimate, stated in the first letter we got from the company, was also a year (end of 2023).
I still plan to keep Hughesnet as a backup, but would like to also have terrestrial internet. All this to say that the wait for your fiber service might be longer than they say it will be. I hope it takes only a year for you, but be prepared to wait longer.