It sounds like your ideal feedback form would consist of your team's standards for "being a good team member" in the form of Y/N questions. I suggest that you take that question to your team directly, either as a form of retrospective or in a separate meeting:
- What are the standards to which each of us should aspire as a team
- What are examples of team member behavior that you find particularly helpful?
- ...that you think contributes well to the success of the team / increases team velocity?
- What are examples that you find particularly unhelpful?
- ...that you think creates obstacles for the team / slows team velocity?
I might have people submit answers to these questions, & perhaps others that the team suggested, anonymously on slips of paper, then read & discuss. I would do it anonymously in case some of the unhelpful examples were particularly pointed, which could happen.
The end product would be a bullet list of Do's & Don'ts, or some other formulation, that you could then use in 360 feedback.
The strengths of this approach are:
- it is initially presented in the context of "how do we strive for excellence", rather than anything touchy like constructive feedback
- it is created transparently by your team
- it is specific to your team's context
Regarding that last point... it's not like there's an objective, context-invariant answer to the question "what makes a good team member".
It could also be that after such a discussion, and the formulation of a "team member standards of excellence" that was adopted and posted, you might find less need for the 360 feedback to address issues with individuals. :)