I had been in a similar situation. I have the original 5D and skipped the Mark II because I was frankly disgusted with canon decision to use the AF of my 5D for the Mark II. I had missed many pictures because the AF simply couldn't cope. The 5D AF was perfect for static situations and slow moving stuff, but inadequate for anything else.
I felt that the Mark III is the upgrade I was looking for - in my eyes this is the Mark II or the follow up act to the original 5D. I did pre-order after a couple of days of thought (3rd March) and received it on the 29th.
I am still learning. I consider the Mark III a completely different beast from the 5D and have to re-learn my shooting setup when handling it. It is far more complex. And it makes my lenses seem sharper. This is probably due to more accurate focusing. This should answer your question - do not bother with the Mark II! Just buy the Mark III. I did find that it does focus hunt as much as my 5D in low light. I think canon should have had an AF assist light on the body.
The ISO sensitivity is better than the 5D.
I do have a full complement of L lenses, so I did not have to choose.
In your case I still feel body over addional lenses is the right thing due to focus accuracy issues.
This is contrary to my belief system of lenses over bodies. I had the lenses but the original 5D made it difficult to use.
As far as the Mark III goes I am still learning and will know soon if it is what it's supposed to be (better AF, better low light sensor performance, better weather sealing, etc.).
Here are my thoughts so far on the cons:
1. I did find that the firmware is quite glitchy and has frozen more than a couple of times.
2. In addition they have made it harder to review picture with magnification by now forcing you to press a magnification button, followed by rotating the dial.
3. Choosing the AF point takes an additional button making it slower to do this operation.
4. The AF is fast and locks on accurately, but hunts in very low light - an AF assist lamp would have made a dramatic difference in very low light situations.
5. Lenses I have tried so far are the 85 1.2 II, 50 1.2, 24-70 2.8.
I will try the rest of the lenses in the next couple of days notably the 70-200 2.8 II and the 16-35 2.8 II.
More to come later.
6. It drains batteries faster than the 5D. Fortunately I had ordered a spare battery. I did pre-order the grip.
I use my original 5D with a grip. It balances better with heavier lenses.
I have decided to rent a D800 with a Nikkor 24-70 2.8 for the next weekend to see what the fuss is about.