@cincystache, the 750W that I bought is a Rad Power Bikes "RadCity" model. It is $1,500 new - but you might be able to find some on the second-hand market for under $1000.
Interestingly, you weigh the same as I do (although I'm only 6'2"... yeah I need to lose 20lbs). I would definitely not recommend a 250W bike for someone who weighs over 200. 750W is a decent amount of boost, but 1000W would be even better.
Have you looked into MMM-style retrofit kits? If you already have a bike that you'd be willing to convert, that would be the cheapest ratio of dollars per watt.
My bike commute is 8.5 miles each way, and on the e-bike it takes about 35 minutes each way. I also bought one to reduce sweatiness in the summer months, and it does work to an extent. That being said, I have one "nemesis" hill on my commute (7% grade for 3/4 of a mile) and though it's not particularly hard from an exercise perspective, it is always enough to get me huffing and sweating anyway, even with the e-bike.
Best thing you could do is find a local bike shop that has a demo e-bike, and take it for a 4 mile ride similar to your commute to see if it solves the problems you think it will.