Dave, First let me correct something in the op. The symtom(s) are in fact there when stopping the car with the gearshift in neutral.
I took it to the dealership today and spoke with the service manager. Firstly he said he has never heard of this type of problem before and couldn't surmise what's causing it. A "professional" would have to look at it. I asked him to take a quick test drive around the parking lot and he said no, that wouldn't help. I suggested that he would be able to help future customers if he experienced first hand what was going on. He then agreed to drive it. Afterwards he commented that it felt like the anti-lock brakes were kicking in.
Of course the next step was to have it diagnosed @ $136.00, which I politely passed on.
I'll have a look at the service manual and see if I can pull the fuse, or something else, to disconnect the anti-lock feature temporarily.
I fthe symotom dissapears then there's the problem. Now that I know it does it in neutral, I'm inclined to think that's the culprit.
Lastly, I was talking with my neighbor earlier, who has a 2000 RX300 AWD, and, lo and behold, they have exactly the same problem.