Jeff,
We did quite a bit of research before starting our Old Dominion line of corn cob pipes. The corn that was traditionally used for making pipes would not have been the modern hybrid "sweet corn" that you buy at the grocery store today. Missouri Meerschaum (MM) uses a hybrid corn for their pipes, but it is a special white hybrid corn developed through the University of Missouri specifically to produce thick cobs suitable for making pipes. Traditional 19th century cob pipes were made using Indian corn which was the most common variety of corn planted in the 18th and 19th centuries before modern hybrid varieties offering higher yields and sized for ease of mechanical harvesting began to relegate Indian corn to a more "novelty" status in the 20th century. Other than the hybrid variety that was developed for making pipes, most modern hybrid corn has been developed specifically for higher kernel yield and thus the cobs tend to be rather small and not ideal for pipe production. We use an heirloom variety of Indian corn that has been grown in our region of Virginia since the 1870s. The variety almost went extinct a few years ago until my brother discovered it and was able to save it and begin to cultivate it on our farm. We consider our variety somewhat "proprietary" and do not sell the seed to the general public.
Re: stems, traditional corn cob pipes used reed or bamboo stems. Early cob pipes often used rivercane (canebrake) stems (often referred to as reed stems) which once commonly grew throughout the South and Southeast. Rivercane is a native American bamboo and was also used for stems for 19th century clay trade pipes. By the 20th century you begin to see cob pipes made with bamboo stems other than rivercane (this may have been as a result of rivercane becoming harder to find and in insufficient quantity to meet commercial production needs). Eventually the bamboo stem gave way to the wooden stems with mouth bits. Interestingly, in my personal collection I have a store display with original MM bamboo stem cob pipes that probably dates from the late '30s to the '40s and interestingly the display features the drawing of a man smoking a cob pipe and the pipe he is smoking has a mouth bit even though the pipes on the display all have bamboo stems! It was apparently a "transition" period and the bamboo stem pipes at that point were most likely considered "economy" pipes in their pipe line.
Cob pipes can be "natural" or they can be sealed with Plaster of Paris and coated with lacquer. It is my feeling that Henry Tibbe and his early cob pipe competitors began to seal their cobs with Plaster of Paris for a couple of reasons. First, Indian corn cobs, though thicker than many modern hybrids, are still relatively small and if you want to bore them out to a fairly large chamber size (3/4" seems to be a popular chamber diameter size in cob pipes)you can very easily end up with thin sidewalls and porous spots within the sidewalls of the chamber. By applying Plaster of Paris you in essence seal up these thin and porous spots within the sidewalls. Second, by applying Plaster of Paris and allowing it to harden, you can then more easily sand and shape the cob on a lathe providing a smoother "meerschaum-like" finish (remember that Henry Tibbe was a woodworker by trade). The lacquer coating then simply seals in the Plaster and protects it from air and moisture. A natural cob will perform just fine as a pipe (our Old Dominion line of cob pipes are all natural and MM offers several of their models with the natural option as well). With a natural cob you can be limited into how wide you bore out your chamber and typically will have to use a smaller chamber size so as not to compromise the integrity of the chamber sidewalls.
Best of luck with your project.