So far I've narrowed it down to a Vstrom, a Versys, and a KLR. I'm 6' 4" and 300 lbs with a 34 inch inseam. I think any of these three would work for what I have in mind but they all seem to have obvious limitations.
These were the three bikes on my short list ten years ago when I decided to get back into biking after 25 or so years away.
I had ridden my son's KLR around town and on some trails. I didn't think I could live with the sound of that engine's exhaust. It was horrible, and this from someone who owned the SR500 single in the avatar, with stock and aftermarket exhausts. Why does the KLR sound so asthmatic compared to the old Yammy. This was to be my one and only bike, and I had concerns about highway riding.
The Versys: One good look and two minutes sitting on it at the dealer's was enough. No No No! Mechanically fine, 17 inch front wheel not to my liking, way too restrictive for movement on the bike. (6-3 and 225 lbs at the time). Plastic covers over the frame to make it look like something it wasn't assaulted my senses.
DL650 had most of what I wanted, and is what I bought. Turned on by them since they first showed up. Seating position was a minus. A big one. I like to move back and forth (and side to side too) on the seat when riding and felt confined. Fixed with a custom seat which does not have the scooped out section, but is virtually straight from front to back. Only good if you have the leg length for it. ABS is nice, but I pull the fuse when seriously doing off road. Big deal is the selection of tires. I have used stock, Michelin Pilot Road 3, Michelin Anakee 2 and Full Bore (similar to Shinkos). On road handling from quite good to excellent (by my standards). Gravel and off-road handling varied from barely usable to quite acceptable. I have a set of Mitas E-07 ready to spoon on, and expect these will do the dual duty quite well. Plenty of after-market goodies for the Strom (and the KLR too, seemingly). Only time I felt the bike needed more power was riding fully laden with camping gear keeping up with traffic at 130-140 Kph into a fierce head-wind for two hours steady. The VStrom 650 should pull your weight as long as you respect its limits. Suspension may need upgrade, but such is the case for all of these bikes, I'd think.
I haven't felt the need to upgrade the springs, but I am now 85 pounds shy of your weight.
Of the three again I would pick the Strom. Great for commuting. With tires like the E-07 (and to some extent the Full Bores) you will have be adequately shod for your purposes; especially since you have that other bike for longer highway use.
That stock seat will be murder, and most of the seats offered may be fine but do not allow the freedom of movement I need and that you may want. At your size you will have to do something about the seat. (The newer DLs feel as bad to me when sitting on (in) them at the dealer's). Sitting so much higher now, and with a long torso, I needed mods to the windscreen as well. (I have yet to sort that out completely).
In short, the Versys miserably failed ergonomics and aesthetics tests, KLR sounds horrible and is lacking on the highway, Strom (of any ilk) needs mods but is best choice. In my humble opinion based on an incomplete data set and fraught with bias.