I've been very curious about paddling techniques that indigenous peoples would've used to propel their craft. Obviously for them, paddling wasn't for leisure or style but for practical functionality. Bark canoes had no seats so kneeling low in the boat resting on the heels was the known position. This of course puts you much lower in the canoe than resting on a seat and automatically changes the paddling dynamics. Here's a great photo of the "Indian's Position" found in Robert E. Pinkerton's The Canoe: Its Selection, Care and Use (published 1914).
Being closer to the waterline forces you to reach lower on the grip for comfort, otherwise your top hand stretches up too high and can quickly cause fatigue. Documentation of this is very scarce but here are some photos I've been able to find which show a little of the grip method. Usually, the paddlers are very low in the canoe, either kneeling or completely seated on the bottom of the hull. This places them much lower than modern canoes equipped with seats. The paddle tends to be held out a but laterally and the grip hand resting more naturally in line with the lower.
This previous post shows some Ojibwe women in their bark canoe. The bow paddler is resting her grip hand along the base in this relaxed position....
Zimmerman, Charles A. of St. Paul, Minnesota
SPC BAE 4605 01601913, National Anthropological Archives, Smithsonian Institution
The October 1990 cover of Wooden Boat Magazine features famous cedar-canvas canoe builder, Jerry Stelmock paddling this style as well...
I've got some more unedited video from mucking around on the lake this summer. I'll try to edit and maybe get another youtube video up.