Oh Jeff, I hate to shoot you down friend, but I'm going to.
I would recommend against a Kono HD for your 1st choice as it is not known for being a "strong" blade. Granted, if you are careful you should never have any issues, but when someone makes "strength" a requirement the Kono HD is not exactly the first thing that comes to mind. Otherwise, it's an incredible blade and to me represents one of the best production gyutos out there. The same argument holds true for the Kohetsu.
For your 1st choice, a strong blade that is full stainless would be a Masamoto VG series: http://www.chefknivestogo.com/mavgsekn.html
(granted these don't have wa-handles). That's probably the strongest blade I would recommend. Still takes a nice edge and it's a great workhorse.
For a knife with a carbon core and stainless cladding I'd recommend the Hiromoto AS http://www.chefknivestogo.com/hiasasustkn.html
(without the thinning of course for increased strength). The steel in this knife is reactive but is much harder than most anything you are going to find in the carbon world. It takes and holds an incredible edge. You will be well rewarded for just a little bit of extra maintenance. This steel will be considered a little bit fragile due to its hardness though, and again this is a western and not a wa-handle.
For a full carbon wa-handled blade, the Tanaka Sekiso Damascus if excellent: http://www.chefknivestogo.com/tanakadamascus.html
It has an excellent grind and wa-handle while not being too thin behind the edge.
For your second choice: If the Victorinox fits your fancy, then by all means you should probably get them. There aren't any cheaper blades on the website to be honest, and for your needs they will probably suffice. If you wanted to spend a little bit more and get something nice I would go with a Tojiro DP 210 gyuto. Hands down one of the best bang-for-the-buck knives out there, and absolutely great for people just getting into the world of high-performance knives. http://www.chefknivestogo.com/tojiro-dp-f-8081.html