Here's an update to my saga.
Recap: I ordered at 12:07am on day zero and never received any communication from Tesla, other than, months ago, I was texted instructions to make sure my trade-in info was complete. The only thing showing on my account page was the "Lemon Law" PDF.
White/White/LR/20"/no FSD
After hearing of people getting their car a week after ordering, I called Tesla two weeks ago to make sure there weren't problems with my order and to ask why I seem to be so far behind others, despite ordering so early. I was told, "at least 8-12 weeks".
Buoyed by the reports here, on 6/7/20 I cancelled my initial order and immediately re-ordered the same exact car (although without a trade-in this time). Right after ordering, an "Order Agreement" PDF appeared on my account - something that I never got on the first order after 15 months.
Anyway, today I got a text from Tesla telling me to expect "delivery near the end of June". The text was worded a little differently than what most others are reporting. Still no VIN in the source code, but at least things seem to be moving. Still can't be 100% sure, but I think I did the right thing by cancelling.