Are there specific animals you are trying to photograph? For birds, a 300 mm lens is considered pretty short, but you still need to be fairly close even with a 600 or 800 mm.
You state that you are not blessed with stealth. Often the only stealth required is the time and patience to sit and wait a long time. Sneaking up on animals for photography is often not very feasible (and for many species not particularly safe...but hopefully you've considered that already).
I wouldn't recommend teleconverters unless you're starting with a fast lens. A maximum aperture of 5.6 is pretty difficult to use with a teleconverter as the viewfinder gets very dark and the exposure is very constrained by the additional loss of effective aperture. Better to make use of the lens as is, or concentrate on getting a used manual focus 300 f2.8 (not as expensive as the latest AF versions...) to start out. A teleconverter on that will be more useable. But I wouldn't do any shopping until you get some real sense for whether your technique is going to be successful and you are interested in this type of photography for the long haul. Fast lenses are heavy and make exorbitantly expensive paperweights if you don't plan to use them...
My two cents.