-- Last Updated: Dec-06-12 2:06 PM EST --
To start out, you have some slightly-erroneous ideas about paddling mechanics. The idea that a blade could supply "too much" power to be useful when soloing isn't correct because with proper technique, the turning force applied to the boat is very small. What little bit of turning force can't be avoided is cancelled-out by corrective action in controlling the paddle, usually at the end of the stroke (but various kinds of corrections can be applied during the beginning and middle of the stroke too). These same correction techniques can be used when paddling tandem, more commonly by the stern paddler, but there are plenty of things the bow paddler can do as well. On a related note (mostly) regarding solo paddling, some boats tend to track pretty straight while others are "eager" to turn. A boat that's eager to turn will veer way off course if even one stroke is poorly done, while a harder-tracking boat might need ten of the same poorly-done strokes to be affected as much. This is just to illustrate that how the paddle is controlled is the main thing.
To get to my specific ideas about blade size, I have noticed that some smaller blades do not "grab" the water well enough for some of the strokes I do at times, and in those cases a bigger blade is nice. How big? I see no reason to go any bigger than the blades of my whitewater paddles, ever, and my favorite cruising paddle that has a blade that's just slightly smaller is perfect for me. If I were at home I could give you the blade dimensions, but I'm guessing the whitewater blades are about 8.5 inches wide (or "maybe" 9 inches) and 16 or 18 inches long.
Racing paddles tend to have rather small blades, and that should be a clue that size isn't the whole story. You CAN get all the power you need from blades that size, with the right technique, and racers like to take very short strokes at a high number of strokes per minute, so I'm sure the extra weight of a wider blade, as well as the extra resistance of blade entry and exit in that case, makes more of a difference for racers too. Such paddles might not start the boat as fast, but do well once underway. I think a person is more likely to notice "slippage" when making abrupt maneuvers than when looking for sheer forward power while cruising along, and I think that's part of the reason whitewater blades are bigger (they also might be bigger so they lose less grip when the water they are in is partly full of air).
I don't doubt that your cheap paddles don't grip the water well enough, but I doubt that it's necessary to use wider blades than what's the norm for good examples of modern paddles. Look at the blade sizes of well-known paddler makers, and you will see that very few of the modern designs (blades that are not very "tall") are wider than about 8 inches (again, that's an "eyeball" estimation from memory, since I can't actually measure any blades right now). I think the efficiency of good technique applied over many strokes outweighs any extra grip that can be provided by brute force for occasional strokes with an over-size blade. You really can't pull THAT hard, thousands of times per day, to get an advantage from all that extra grip on the water provided by a bigger-than-normal blade.
That's my non-scientific view. I'm sure someone has analyzed this pretty carefully though, and yet no super-sized blades were invented as a result.
Oh, one more thing. Your canoe will only go so fast. As you approach the boat's theoretical top speed (called "hull speed", in case you want to read about it), each increment of additional effort you apply provides less and less additional speed. Wind is another issue, and more paddling power will do more to increase your speed into the wind than it will do to increase your speed through the water. This just helps to show that nothing is black and white though. I'm as interested as you regarding how "ideal" blade sizes are chosen by designers.
Okay, here's "one more" thing, and this time I think I'm done. I have noticed a mistake by a lot of beginning paddlers, and I made the same mistake with my first "good" rowboat, which I bought a couple years before any of my canoes. Again, this has to do with the boat's maximum speed. People tend to want to "paddle harder" to make the boat go faster, and often they don't realize that their speed has already entered that realm where large amounts of additional effort result in very little additional speed. There are two ways to "cure" this problem. One is experience and lots and lots of time on the water. The other is a wonderful shortcut called a "GPS". Monitor your speed with a GPS, and you will quickly figure out how much of your hard work "just isn't worth it" in terms of realized benefit. It might turn out that you change your mind about needing extra paddle power. You might be working too hard for the speed your are getting no matter what paddle you use.
My best advice is to buy some decent paddles - "real" paddles rather than what can be gotten at ANY big-box store (stay away from places like Dicks and Gander Mountain too!). Get them in the right length too. THEN start experimenting with various degrees of effort and the speed you go as a result. It might be a good idea to learn about the basics of stroke efficiency too (and since I mentioned it, here are the basics on stroke efficiency in a nutshell: For each stroke, the shaft should be vertical as seen from the front or back (not "reaching out" to the side at all). Each stroke should be in a straight line that is parallel to the long axis of the boat, not following the curve of the gunwale. Each stroke should end before your lower hand passes your hip (racers don't even let the blade go past their hip) so that you don't waste energy "lifting water". I break that last rule quite a bit to improve correction leverage, but it's a good rule NOT to break when you want the most forward power per energy expended).