It sounds like you did it right except you waited way too long to restart the kombucha.
The culture needs a constant supply of Sugar and tea to stay alive. It takes 9-12 days for a three quart batch and 7-9 days for a one quart batch.

You don't have to wait for the original culture to drop to the bottom of the jar. That usually doesn't happen. Just peel off the newest culture and use that for your next batch. You can re-use the same culture several times, but the strength of the kombucha will diminish if the same culture is re-used too many times.

Since you have waited so long, I would suggest using both cultures in your next batch. You can leave them joined, it won't hurt anything. If no mold has grown on your first batch, it should be safe to use some of the kombucha you made to start your next batch, but I probably wouldn't drink the second batch because of the age of the kombucha. As soon as your second batch is done, start a third batch. The third batch should be safe to drink.

I know this is an older post, but in case anyone else has the same problem I am thought I would answer.

It's still safe to drink, but it will taste very sour! You can use it in cooking as vinegar, or add lots of water to it and drink it, but again, the taste is not so good. Making a second batch with the same mushrooms is totally acceptable. As long as it has stayed moist, it should be preserved.

The only times you should worry about reusing a mushroom is if you have grown mold on top. It would be green or white and fuzzy, just like other mold you have seen. Throw it out if it does, and also if it gets fruit flies!