"How big of an explosion in exploration do you mean? I'm sure there will be several occasions when a new system will allow a significant growth in exploration. I'm thinking about the critical change where private companies and even individuals will be able to conduct activities in space as easily as they now conduct activities on other continents, without any governmental support."

Hmm, this is quite a difficult question for me, but I'll give it a shot.
Big explosion- like internet only bigger and longer lasting. But would involve government. Government would do things which encourage private sector in a number of ways [reduce risk, exploration, technology testing/demonstation, and being a buying of some products which would align to national interest].
As far as total of investment in space infrastructure private sector would be providing most of the funds. Government would be investing money so as to "build confidence"/reducing start up risk- in number of ways. I see NASA using the private sector and private sector using NASA- a symbiosis. NASA can't be the only customer but it can be a customer.

"I'm no big fan of NASA myself, I was just using their stated goals as an example. I'd be delighted to see other approaches worked out by private concerns. But even so I don't see that a much more accelerated time line could be achieved."
Well, once it was demonstrated that some aspect space development was profitable, there could become a large amount of venture capital which could become involved. Though NASA has large sum of money to spend each year on space, capital markets have much larger sums which can be invested if there is a possiblity of good return.

"Laser Lightcraft are only intended to lift one Kg or so to orbit. For larger masses a Microwave Lightcraft can, theoretically, be used. The energy equations for such a device do work, but the technology still has a long way to go. There is also the possibility of the Space Elevator. Again the energy equations are sound, but the technology is not there yet. A long shot maybe, but who knows. There are no doubt other possibilities that no one has thought of yet."
I guess at this point I should talk about my pipelauncher idea, but I guess, I'll pass:)

"My point is that as long as we stick to the idea of carrying your fuel ( the rocket paradigm) the costs will never drop as much as they need to for space travel to be worth the expense."

Ya, it kinda of the idea I'm talking about. Ultimately you would get water from the space environment (moon and asteriods). But first you would start by getting water from Earth using cheapest possible means of shipping it up there. If this "turns out" to be $500 per lb, and if there is market demand for water at this price, then this means that water is worth $500 per lb- meaning if you could get water to orbit from other than from Earth it's still be worth 500 per lb. Meaning if some space rock had about million lbs of water locked up in it then it's got around 1/2 billion dollars worth in water. Million lbs of water isn't much water, the Moon has a estimated 6 billion metric tonnes of water at both poles. And a few asteriods are are thought to have as much 25% of their mass as water ice and if a space rock is only the size of a mountain that's a lot of water.
With more supply of water in orbit the price will drop (which means the price of getting beyond earth drops). But even at the price of 500lb water you get could get significant reduction in mission costs- depending on costs of building & maintaining a gas station.

"I'm not sure I entirely understand your water scheme, but if it would result in greater investments in developing conventional and unconventional launch technologies then I'm all for it."

That's what it does.