First of all, I think itís great that you are trying to modify your camera to get what you want out of it! Tinkering with cameras is something of a hobby of mine, especially old medium format viewfinder cameras from the '40's and '50's. Some of these are distinctly lo-fi and others not so much; but typically they sport simple single-speed shutters similar to yours. I can say that in my experience there is almost always SOME way to increase the shutter speed, at least to within a factor of two or so.
In the case of a swinging paddle shutter like yours, the first thing I would suggest is to make sure the mechanism is as clean as possible, especially between the paddle itself and what it is sliding on. Any dirt or dust in there will slow it down, as will (perhaps counter-intuitively) any oil or grease.
Other than that, spring modifications are the most obvious thing to do. For a tension spring like you have, shortening the length is the basic way to increase tension and thus speed things up. Rather than doubling the spring over though, I think you might have better luck if you simply cut the spring to a shorter length, then bent and reformed the cut end to match what was there before so it can hold onto whatever it is connected to. You want to make the spring motion as smooth as possible, trying to avoid coils sliding over any surface, or having coils catching on eachother. Admittedly, cutting and bending springs tends to be kind of fiddly work. But if you have some needle nose pliers and a little patience, it is really not that bad. I do it all the time!
As others have mentioned, if the moving disk or blade (or whatever the shutter uses) has a slot or other opening in it that lets the light through, one of the easiest ways to increase the speed is to mask that opening to a shorter length. But I donít think thatís what you have, so probably a moot suggestion.
Limiting the range of motion is another good idea, like you did with the piece of balsa. I hadn't thought of that one!
A final technique I can think of is to lighten the moving parts where you can. If you can remove the blade, you might be able to drill holes or clip edges off of the paddle to lighten it, provided that the cuts do not let any extra light through the hole as the blade moves. You could also sand the surface of the paddle to remove material. Granted, these are pretty desperate measures and honestly, I haven't tried them. But in theory it should work!