21 vs 40 ksi yield strength is a big difference for a frame that is supposed to resist bending.
Seems like the answer is to get 6061 T4 and heat treat it at home to T6 after forming.
Discussion
whether it's a big difference or not, it may still be plenty for the application in the tubing sizes that are practical to use
and it's unlikely you're going to heat treat to T6 at home, the process is not trivial
anyway my point isn't that you should use specifically 3003, but that materials should be chosen based on their strengths. this application does not play to 6061's strengths, it's just an alloy people know about. so use something that is either formable cold, or that won't be negatively affected by local heating
and either way you should be using a tubing bender that supports the walls of the tubing to prevent kinking and flattening, if you're trying to push the limits of the material. the most important thing here is keeping the tubing tube shaped through the bend