"Can you suggest a mature man-rated technology that can give significantly shorter travel times, or are you tripping yourself?"

Yes that's what I had in mind, a mature man-rated technology- which is another way of saying of using chemical rockets.
If you want to go to Mars, go to the Moon first. The Moon probably has billions of tons of minable water. Water can be converted into LH&LOX.
The Moon is close to Earth and the Moon's gravity well is significantly less than the Earth. NASA mission: go to Moon, find out about some details of these hydrogen deposits [most likely water ice]. NASA's budget for this mission: 5 billion. Start now, be done by 2007.
Engage.
:)

[ I wrote the following and decided I not to delete it]:
The only advantage of any technology is that it lowers cost or has the potential of lower costs or the flip side increases or has possiblity of increasing profit. This applies to space technology or farming technology- a tractor is of little value if oxen can give more return- plow more acres of land for less overall costs.
Unless "something dramatic happens" it's not reasonable to expect that NASA could do a Manned Mars for less than 100 billion- unless there is a unexpected advance in technology that allows this to happen or the "game is changed". Rather than depending on some unrealistic technological magic bullet I tend to think that changing how NASA approaches the problem is a better solution.
Now, there is a simplier solution than changing how NASA does things [and that is do what it "always" does]. This can be seen as a war of attrition. All NASA needs to do is continue to exist- get it's 15 billion per year. This approach will end up with a Mars mission costing far more than 100 billion. [But high costs are not really a problem, justifying NASA's existence and getting a bigger budget is the only important goal.]
So if a Mars Manned mission was "done right" it will cost around 100 billion- this means NASA gets the go ahead and continues to get enough funding year after year AND has a limited mission (not colonizing the planet obviously, and if you want a permanent research base this cost would need to be added on top of the 100 billion). This wouldn't be too bad, but it's unlikely that this would actually happen. The more likely result is like how NASA did ISS.]
Bah bah....