The Swift scopes are well-made, with excellent optics (much better than one would think, given the low price). I have used them for years...and never experienced any problems. I think that you will be pleased with a Swift - about that, I wouldn't worry, if I were you.
As to the type of scope, I agree with others here. A 2 - 7 x 40 is a bit large for heavy brush hunting. As another poster said, you should consider Exit Pupil very closely, especially for this application. A 32mm objective would likely be easier to mount low on the rifle, but you do lose a lot of Exit Pupil with a 32mm scope, ABOVE 4X magnification. You are on the right track, though, when you said that you could use just 2X or so, in the woods....and turn up the magnification in open country, or when target shooting. That strategy will certainly work. At 2 - 4X, the Swift scope that you are considering will provide lots of light and field of view, so that the scope will not hamper your shooting in low light levels. I think that you should go with the Swift, as long as you are able to mount it low enough to be comfortable to use. If not, I would suggest either of the Swift models 665 or 648. These are 1.5 - 4.5 X 32mm scopes. The 648 is from the Swift Premier line... and a bit more expensive than the 665 (but still cheap, by Leupold standards). Even at 4.5X, you will still have more light than you can use...and the 32mm objectives will allow a lower mounting on the gun. You don't need more than 4X, really, for accurate shooting out to 100-150 yds. Just a thought.
In summary, I would say go with the Swift you chose - if there are no mounting problems. I have a feeling, though I can't prove it, that you can mount the 2-7 X 40 scope with MEDIUM rings. This would likely allow a good cheek weld on the stock when shooting. I used a Swift 6 X 40 on one of my rifles for years (a Rem. 700) and medium rings were as high as required, even with the long bolt throw. With a 7600, you have no bolt to operate manually (thus, no scope interference issue) - so, I think most medium rings should work.