50mph and $1000 budget don't really meet at any point. I ran your weight and estimated bike data through the Kreuzotter speed and power calculator. You need about 800W to the ground to sustain 30mph on the flat. 1800W will get you a steady 40mph, and to go 50mph, you need about 3500W-- real mechanical power to the wheel, not electrical energy at some arbitrary RPM. That means to sustain 50mph in neutral conditions, on level ground, you'll need at least 5000 real world electrical watts, and you'll have to do a good job of load and speed matching.
Short version is, you won't get a motor and controller that can take 5000W, Plus a battery that can provide 5000W, for anything close to $1000 total.
If you play your cards right, you can probably get a motor kit and batteries for $1000 that will build into a 35mph bike with enough range to do your round trip. The bike won't be very pleasant at that speed, but it should hold up ok.
For 50mph, the battery alone won't fit in your budget, and the bike won't hold up worth a damn either. None of the motors I know of that can put out 3500W will fit in your road bike frame.
You are on the right track about one thing-- above 35mph cruising speed, you don't need to trouble yourself with pedaling. It costs more in aero drag to pedal at those speeds than your pedaling will contribute to total power. So it might as well be a scooter.
Familiarize yourself with Texas Transportation Code Chapter 551, Subchapter E. That's the part that governs motor-assisted scooters. It's more permissive than what's allowed for an electric bicycle. Know the law and be ready to cite it to a cop.
https://statutes.capitol.texas.gov/docs ... TN.551.htm