I'm also 6' 2", 73 years old and 260#. Due to back & joint problems, I require an upright riding position and a bike that would handle my weight plus the 40# of cargo I sometimes carry. In addition, I have circulation issues which require the use of good suspension and a nose less seat. I spent all of 2016 and part of 2017 ebike shopping. I test rode dozens but was unable to find a suitable model. I finally picked a bike that filled most of my requirements and was easily modified to handle the rest.
I chose this Pedego Platinum Interceptor:
Discover the perfect electric beach cruiser with the platinum edition of Pedego's Interceptor e-bike, offering unique style and a 5-Year warranty.
www.pedegoelectricbikes.com
This bike has extra long control cables to fit it's "moustache" style handlebars. That made it easy to add a stem riser and more suitable bars to get the upright riding position I need.
Although I can still swing a leg over a high bar bike, I don't know how long that will be the case. For that reason I went with a step thru model. I also chose the mag wheel option to better handle my weight requirements. It's a $400 option but may not be necessary in your case.
For me, the seat tube height was also critical. I needed 4" of seat tube clearance to allow the use of my Kenekt Bodyfloat and Thudbuster LT suspension seat posts. With the posts installed and adjusted for my 6' 2" height, I still have almost 3" of seat tube clearance.
The bike lacks rear suspension but the quality seatposts I use are a good substitute.
The list price of the bike is at the top end of your price range but I found many dealers are willing to deal. I paid $3900 for mine in 2017.
Here is a pic before and after the modifications.
The mods cost less than $100 and took 2 hours to complete using just a screwdriver and allen wrench.