How to I go from absinthe jailbreak to evasion jailbreak?

I have an jailbroken ipad 3 IOS 5.1 (absinthe) and want to upgrade to IOS 6.1 evasion jailbreak. I want to be able to restore my ipad backup after the jailbreak if possible.

What is the best way of going about this?

I am thinking about doing it this way. Please tell me if my method is wrong.

1. Back up ipad to computer.

2. Install IOS 6.

3. Setup as new ipad.

4. Jailbreak.

5. Reset ipad settings.

6. Restore from itunes backup - Will this remove the jailbreak?