I can confirm trade in does hold your car up. Almost same situation. Ordered April 28th. Wanted to trade in car so I filled profile. On July 10th I requested to have the trade in remove as teslas offer was substantially lower then KBB and surrounding dealerships.
My EDD just disappeared. Thought okay they are updating system. Got tired and impatient and called my service advisor.
Thankfully I did. Someone didn't do their job and removed the trade in but left trade in open. Meaning profile was not complete. It literally put me to the back of line and said November delivery. Talk about upset. I was transferred to someone who put me on "high priority" and apologized. Model Y LR White ext black int, tow hitch, 19", no FSD.
They really need to fix their system. Numerous times I have got close to just getting something else. I recently sold my model 3 performance. So annoyed that because someone at Tesla didn't do their job, I get "punished" for it.