We went with USAA, they approved it nearly instantaneously. I requested a loan for an amount of what I wanted - which had me coming up with the rest as a downpayment. The approval came back 10k more than I asked for. They did not require me to upload the purchase agreement at that point. They then gave me a dealer funding request form that I was supposed to send to the dealership. This is what they use instead of sending me a check - it's the dealership's responsibility to send the form in with their bank account and routing numbers, along with a signed purchase agreement (by us as well as someone from the dealership / Tesla) and some document that shows they've applied for a title with them listed as lienholder, then USAA sends the payment electronically. Apparently they funded the loan on the wednesday following our sunday delivery.
After that was initially approved, I used the online chat feature to tell Tesla I wanted to switch from cash to third party financing. They asked me who the lender was, how much I planned to finance. At that point my account showed that I owed the downpayment. I waited until delivery day to pay the remainder.
As for the downpayment, I did that by bypassing plaid on the day I took delivery, just entered my ACH details in the parking lot after I looked the car over.
Just two, Erie is our current insurer and they came in about the same as our Audi, the other quote was a lot higher (forget who that was with now)