From what you are saying the engine runs fine. So I wouldn't bother with checking injectors, maf or any of that. Since your transmission seems to be fine after it runs a bit I wouldn't think anything major is wrong with it either. I'm no tranny expert, I'm hoping with your further explanation someone who has had the same problem will chime in. What makes sense to me is something is sticking like a valve in the transmission valve body or a shift solenoid is going out. Is your runner a 4WD? Have you tried shifting the transfer case through the gears, 4Lo, 4Hi, back to 2Hi? The link below is from another forum, this guy said his problem was one of his brakes sticking. You could try backing into your spot and then you can go straight into Drive and see if it changes. Try putting it into 1st or 2nd to see if that makes a difference. Search around in other forums and this one. You'll probably find lots of things to check out.
http://www.yotatech.com/f2/help-3rd-gen-problem-44657