Regardless, do write (not e-mail or phone) ATF, describe exactly what you are making and why, and why you feel it will have a genuine sporting purpose that a gun under .50 caliber won't fulfill. Note that the reply may take a while.
You should receive a reply in writing. If you get approval, it will be in writing also. You probably won't need dozens of copies, but keep the original in a safe place. Then make the gun as you described it to ATF. Do not decide to make it full automatic or have it fire nuclear rounds. If you are turned down, best drop the idea and work on something that is not subject to approval by anyone.