Mapping a gravity form to a membership level

Hi... I'm hoping someone might be able to help me here. What I'm looking to achieve I think should be relatively simple however from a lot of the searching and reading I've been doing I'm not so sure. I will try and explain:

I have BuddyPress working with the Membership plugin. All fine and good... I have set up 3 membership levels, for the purpose of this let's call them something creative like Membership #1, Membership #2 and Membership #3.

I have installed Gravity Forms (Developer Edition). What I'd like to do is the following:

Create a form using GF (called 'Membership #1 Sign Up Form') and map it to the membership level 'Membership #1'

Same thing for 'Membership #2' and the same again for 'Membership #3' - so all membership levels have different Gravity Forms.

GF really just acts as the front-end form engine.

I hope that all makes sense. Any help would be greatly appreciated as I don't particularly want to try and hunt down another solution.

Thanks in advance.