I have tested my 500/4 AF-SII on a Gitzo 3 and 5 series and a Feisol 4 series. In doing a detailed tap test using a D300, Jobu Pro gimbal and the three tripods I found the following.
The 3 and 4 series above are adequate but not optimal for my lens. The lens settled in approximately 4 seconds once tapped. I ran the test several times to verify the results.
Tap tests using the 5 series settled in approximately 1 second. The difference of 3 seconds in settle time is significant and tap testing is a non-scientific demonstration of the tripods ability to handle vibration with specific hardware.
Your D800E will let you know quite quickly if your tripod is inadequate for the equipment mounted. As someone suggested VR is the great equalizer but even with VR you may find that the D800E wants the best support possible. You are focusing a lot of MP and the slightest movement will be noticed.
The dilemma you face, as we all do, is stability vs. portability. I own a 3541LS that I use for smaller lenses and travel. I tried it for several months hoping it would be adequate for the 500/4. Unfortunately I was not getting the results I wanted, especially for that lens so I moved to the 5542LS. The move to the 5 series made a significant difference. There is approximately a 3lb difference in weight and a noticeable difference in bulk, both an important consideration and obstacle to portability.
Most of my shooting consists of several hours walking trails in NWR, State Parks and along the shoreline so portability was a major concern for me. While the 5 series is heavier and bulkier the results I get are better so I endure the extra weight. It also allows me to focus on the shot and not focus extra attention on technique, which I found I was doing when using the 3 series.
Which series you decide on will be determined by your specific needs and expectations. As I mentioned above if your lens has VR you may find that a 3 series will be fine. If your lens is a non-VR you may experience some of what I describe.