Simple solution is to prefer to take delivery 2 weeks after the end of a quarter. The local Service/Sales office here in my area has a lot of new cars out front, doesn't seem busy right now and would be the perfect time to take delivery. End of quarter rush? Avoid that.
That's not going to help much because you may still have very poor communication with your DS before the end of quarter if they are overwhelmed with the end of quarter deliveries.
Tesla seems to want to deliver overseas at the beginning of the quarter, so I suspect you'd end up not actually hitting that first 2 weeks anyway as they shift their production towards other territories.
A far better solution is that Tesla stop trying to game their delivery numbers and just deliver cars across all their locations evenly, meaning they'll have appropriate staffing to not get overwhelmed.
From the number of cars placed at this location - it appears they may be wanting to sell direct and not even worry about the ordering process at all. The whole "wait 3-months, check online every day, clicking like crazy" then wanting periodic hand-holding by the DS appears to be a high-cost way to handle car buying (for Tesla). By positioning cars in the field, typically bought by buyers in that region, there is a chance that the style and options you want will be available when you want it - right now. And many are closely aligned - like how member frankness did it before quarter-end.
I'd have taken a car that was nearly what I'd ordered but that was available sooner. But that option wasn't available to me. I don't know if that's because no such vehicle existed or because my DS didn't bother to look for that. I honestly can't fathom Tesla wanting to be out of the ordering business because without ordering you have to guess what people want and then hold inventory. When you make cars in advance you make educated guesses about combinations that people want. From past experience that means some combinations are impossible to purchase. I recall my Mom wanted a blue Toyota Corolla with some options that were never put on blue cars. Toyota doesn't do custom order cars. The dealer had to call Japan and plead for them to build this specific car. They managed to get this done. The VIN for that car included the color of the car and it was wrong. That's almost certainly not the experience Tesla wants customers to have.
I didn't want hand holding from the DS. I needed information so I could plan for my delivery appropriately. My first contact with my DS was to try and get a sense of what Late September meant so I could try and finish up so financial stuff before delivery that was planned to be finished in Early October (well before my expected Late October delivery). If Late September meant September 16th then we were going to have to delay delivery. The second contact was when the date disappeared, something that should have triggered an email from Tesla telling all of us what was going on. Instead I had to call them to find out they'd just removed the specific dates before the car was being transported. And the last time I tried to contact my DS was the morning of the delivery. All of those need to contact my DS could have been eliminated by more proactive communication from them. All of which probably could have been automated.
Tesla as was made clear to me on the phone today wants the DS and the customer to have a personal relationship. Clearly they think this is important for the delivery experience. I doubt they'll remove it for S and X deliveries, but maybe they will for the 3 since it may not scale.
Also, assigning a delivery date by waiting until the car is actually in transit is far better than assigning a Vin # early, assigning a delivery date early and possibly flubbing it up. Vin # should be assigned when the chassis enters the paint department. From there, you know the car is "real". A Vin # three months before production really plays with the buyers' psyche (but works on wall street).
I didn't mention it but she did confirm that the delivery date not being set until car is in transport was a policy change.
However, your suggestion that the VIN be assigned when the vehicle enters paint is not a good suggestion. It's almost certain that the VIN is stamped into the metal before paint. VIN should be assigned as the vehicle starts production.