Car vibrates in reverse only and clunks once on start up.

I just replaced the clutch on this vehicle. This vibration in reverse an the clunk on startup started approximately 100 miles after I finished the clutch.

While in reverse, if go very slow it does not vibrate. It is only when I reverse at a normal speed. Again, this is only in reverse. While accelerating in first gear, there is no vibration.

The clunk happens once right when the engine starts up. It did not happen before the clutch was replaced.

What I suspect it to be is the rear engine mount. Upon inspection, the bottom bolt that attaches the mount to transmission is very close to the part or the mount that attaches to the frame. The engine mounts looked to be in decent condition when I took them off during the clutch change. The long bolt that goes through the rubber part was taken out on the rear mount, but not on the front mount. I might not have put enough pressure compressing the front engine mount when the rear one was attached. So, the engine might be sitting too far back.

Here is a picture of the bolt on the engine mount: http://imgur.com/ioQGv (the image adder down below is not working on my phone)

I think this could be causing the clunk I hear at start up as well. The engine might be vibrating just enough on start up to cause the bolt to hit the other side of the mount.

My questions:

1. Does this sound like a plausible hypotheses?

2. If not, what could be causing this problem?

3. If so, what would be the best way to go about adjusting the rear engine mount so that it holds the engine further forward?