I'd be more comfortable with the Lee Valley kit if it said HSS somewhere in the description. I wouldn't want to pay that kind of money and get something that wasn't. I'm sure their support people could tell you if you asked.
$100+ seems like a lot of money to throw at this problem--I don't know what you're doing (or if it's something you're going to make multiples of, which might sway the decision), but I've been doing fine with these and these for quite a while (and you know I'm a buy once cry once kind of guy).
HSS would be an improvement over that stuff, I'm sure, but I'm not sure you'll get proportional value out of spending 3-4x as much.
Also, I snap those tapered bits sometimes. I would be less happy if I was snapping an expensive HSS bit that was part of a set.