This may not be quite the answer you are looking for, but may I suggest that the actual issue you are having derives from the attempt to use virtual "analog sticks" in the first place.
First of all, if your audience consists of people who are not accustomed to using controllers (I would assume they would be what is refereed to by some as "casual" players) -- then it may very well be that you need to rethink your control method, and design for them. That is, if you are designing for people who play block matching games, and are thus comfortable with touch-dragging or tap-touch interfaces you may want to figure out how to make your game work with such a control scheme.
The other issue is that of working within and around your limitations, not through them. The fact is that virtual controls are (in at least a majority of cases) inferior to the physical version they attempt to emulate. If you are designing for mobile ask yourself if you really have to use a given design paradigm just because you are familiar with it, there is probably a better way -- especially if you think it through.
Absolutely. If your game requires a "virtual joystick" of any kind, you've failed to design properly for the touchscreen.
The problem really is that we're trying to make types of games that play well on controllers or with KB+M, but for a fundamentally different input device.