-- Last Updated: Dec-03-12 9:09 AM EST --
You might want to check out the Qajaq USA paddle poll at http://www.qajaqusa.org/Equipment/paddle_poll.html. You will see a number of people with GP blade width under 3", including the great Maligiaq Padilla.
There is no need to reinforce the loom/roots of a narrow GP. Where the blade transitions into the loom should be almost round, and is quite strong if you use decent lumber.
I find that paddles that are too narrow for me are more prone to flutter and take more skill to handle, but having a blade that is too wide is not any better. The "Goldilocks principle" applies, it needs to be "just right" :^)
A good guide for making a GP, including appropriate cross-sections, is Chuck Holt's Greenland paddle plans, on the Qajaq USA paddle page at http://www.qajaqusa.org/Equipment/paddles.html .