and without running any numbers, here's what comes to mind:

Two metric tons is 4,400 pounds. That isn't as much as it sounds. To launch 3 people from a balloon 38 KM high to over 100 KM, you have to consider the following:

1. How much do the 3 people weigh?

If you're talking about grown men, you're probably looking at somewhere around 170+ pounds each. You could use smaller people, such as small women. Jeanna Yeager, most famous for being Dick Rutan's copilot on the Voyager around-the-world flight in 1986, was supposed to be the first private rocket pilot back in the early 1980s. She was chosen in part for her flying skill and also the fact that she weighed perhaps 90 pounds. That project collapsed in the early 1980s due to a lack of funding.

Anyway, with the tight payload limit of the balloon, you'd be better off with small people as passengers compared to average sized people. You'd also save structural weight because the rocket could be made smaller. However, this could complicate the next issue...

2. What form of life support will you use to keep them alive?

Probably the lightest system would be for each passenger to have his/her own full pressure suit instead of relying on a pressurized cabin. However, small people are less likely to find an available surplus pressure suit that fits. Those suits are expensive. I've read that the suits U-2 pilots wear cost $10 million each. Finding surplus suits would be very important in keeping costs under control. The suits you're most likely to find surplus will be ones that fit average sized people.

A pressurized cabin would likely be heavier and more difficult to build than an unpressurized cabin. You'd probably still want a pressurized suit in case you lost cabin pressure. So, that begs the question, if you're going to have to have pressurized suits anyway, why not just use them by themselves?

3. What form of propulsion will you use?

With little weight margin to play with, you'd probably need a liquid fueled engine instead of a solid fueled system. Most liquid fueled rockets have a higher Isp and that would be vitally important.

You basic design approach would be to calculate the following:

1. Mass of the payload
2. Mass of the life support system
3. Mass of the structural systems, guidance systems, etc.
4. Mass of the recovery system.

Total all of these masses and subtract that from the 4,400 pound balloon capacity. That will give you your mass for the propulsion system and fuel. You'd then need to calculate how much velocity you'd need to fly from 38 KM to 100 KM and plug these numbers into the rocket equation to determine the required Isp which will dictate the type of rocket you'd need.

Off hand, I believe it might be possible to accomplish the mission but I don't have the time to run the numbers right now. Perhaps you can set up a spreadsheet and start playing with some numbers. Here's a link to some references that might prove useful. I'd be interested in seeing what you come up with.

One thing to keep in mind is that the X Prize requires two flights by the same vehicle within two weeks of each other. Those big scientific balloons are quite expensive and are subject to things like weather delays.