Few more thoughts:
If money is taken into account (and it 100% is by far the most important thing, and in some ways the only important thing) - either Hall of Fame, or Hart. Both pretty much guarantee you ~$50M+ career earnings, and probably more. The others could be 10x less, depending on how things shake out.
But for fun - let's completely ignore money. Let's assume my career earnings are exactly the same in any of the 4 scenarios. Here's how I'd rank them:
1. Hart. Yup, still care about this the most. I want to be seen as one of the best players ever, and this guarantees it.
2. Hall of fame. Same idea as above. I want to be seen as one of the best ever, and having a hall of fame career is huge. I like the idea to being the absolute best in the world, even for a short period - which is why I prefer hart. Kind of hard to envision a hart win and no hall of fame though.
3. Stanley Cup.
4. Gold Medal
If it's a Gold Medal as an underdog country and I'm a key contributor (ie Hasek/Jagr gold in Nagano) - I might pick Gold above Cup.
I mention Hart trophy - and I know OP says Hart/Norris/Vezina. Hart is way more valuable for me. If it's not a hart but a vezina or norris, than I would pick Hall of Fame #1, and that trophy #2.
In the end - a team trophy is great, so I'm not trying to diminish what a huge accomplishment winning a cup or gold medal would be, but I care a lot more about being the best I can be and standing out for my own accomplishments.
To make this closer, OP would have to give more details around the cup or gold medal win, and exclude career earnings. Am I the MVP of the playoffs in a cup win, or MVP in a gold medal win? That might be better than a hart.