Cripes. Sorry you have gotten such a hard time with responses. It is clear that you like the property the way it is, so don't listen to the bozos that tell you to bring in fill, change the stream, or whatever. Do what you think you will like best. I personally think your original suggestion was pretty good.
Based on your suggestion, I would think this is not a classified wetland (but, as you can tell from previous responses, it is not always clear). If it _is_ classified wetland, then you may be out of luck. This may be unfair (there are some extreme examples of laws and regulations getting out of control), but it may also be perfectly reasonable in the larger scheme of things (paying some money for a piece of land doesn't give someone absolute or unfettered control over all aspects of the land and its use, especially if the rest of us might be harmed, as would be the case if everyone continued filling in their wetlands). So I'd check the various regulations and ask around a little, and think hard about if you would really be doing significant damage to something that is important to the community. I'd bet you will be fine...
In which case, go for a narrow, raised walkway. Depending on climate (does it freeze hard?), you can get away with some pretty minimal disturbance. I'd be wary of a general deck contractor. Their typical solution to a water issue is going to be just dig big holes (with heavy equiptment) and fill with concrete. After they get done, your nice marshy area will be a huge mud pit, needing extensive landscaping, replanting, and restoration. It will not look the same for years, or even decades.
Here is an interesting, simple idea:
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I have only seen this done once, in NC I think, but it looks pretty easy. The idea is to build simple frame sections of walkway (say, 12' long, and 4' wide), with 4x4 posts at each corner, and maybe 2 more posts half way along, to raise it up off the ground a foot or two or three. In your swamp, a small cone-shaped concrete block serves as a foot for each post, with long metal spikes driven in to the ground to keep it from moving around. You place the blocks, then carry the frame and put it on the blocks, then nail on the decking and railings. When you are all done, there will be nothing worse than a few footprints in the marsh. The blocks might not even be needed, you could just pin the posts at two angles. Think of the whole thing as more of a floating dock -- the sections should be coupled together loosely, to allow for a little movement over time. The gazebo could be done the same way. To get the pins in, you would need either a sledge hammer, or depending on the soil (rocky?), you might even need a small jackhammer.
So ask around, and see if any contractors in your area are willing to try something less invasive than just simple excavating and pouring concrete.