Papa Tony is Da Man:worship: and has a world of experience on our car, but in this particular case I would not immediately do what he suggested.
Consider this: Wouldn't it be best to try to remove as much of the debris as possible before you use a flushing technique that will likely allow the debris to spread into all of the sensitive areas of the trans, like the bearings?
Here's what I would do:
The speedo drive mounting hole in the trans casing is in the differential section of the trans. On the other side, you'll note that both the drain and fill holes are also right there in the differential section.
The good news is that this area is more or less the low point of the trans. My theory is that you will be able to flush out most of the gunk that fell in just by flowing solvent in the speedo drive hole and out thru the drain hole.
I would think that the best thing to do would be to keep the trans in the car for the moment. (If it's already out, then keep it upright and do as little as possible to disturb the gunk that fell in.)
First, clean around the speedo drive hole and the general vicinity to ensure that no more gunk will fall in.
Position drain pans and such under the trans, then drain out the existing oil, noting how much of the original blob of gunk makes it way out of the trans "naturally."
Next, using your shop vac, rig up a nozzle that can fit inside the speedo hole (say maybe some 3/8" or 1/2" copper plumbing tubing), duct tape it to your shop vac hose, and suck out what you can of the debris.
Then, using Tony's idea of some sort of solvent (I'd probably use gasoline), keep the drain and fill plugs out and start pouring the solvent into the speedo hole, again looking to see how much more gunk gets flushed out.
After flowing some solvent and judging how much gunk is getting flushed out, make the decision as to whether you want to proceed with the full flush that Tony wrote about.
