my best guess - and it is only a guess :
If you have an End of June delivery date you would already know about it, and be having to "Send Cash Now"
If you have a VIN then my guess is you have a July delivery date, and you would also have had a call confirming approx date e.g. "Mid July". (That includes a VIN hidden in source code and not on official documents ... yet)
If not then i doubt there will be (many?) deliveries in August. Tesla has been hell-for-leather satisfying USA order at end June, end-of-quarter, so will have been manufacturing for that market. So if I assume zero cars made in June for EU / UK market then zero deliveries in August. So then it will be September (This is backed up by a lack of VIN's allocated for RHD cars recently ... )
If you change and IF you go to the back of the queue, then it will be September I reckon ...
But you might also change to a model that they have ample stock of, and get an earlier date ... altogether i don't think you are going to bump someone who already has a VIN ... but you might get their VIN if they are bumped (a delay getting finance, for example) if you are higher priority than someone else (early reservation holder etc.)
Everything you say rings true. When I spoke to the Tesla sales chap he was saying that demand slumps in August due to folks waiting for the new registration (does anyone still care about that anymore ?) and so deliveries could move to September. I think it is a nice scripted excuse for late deliveries. I don't have anything, no VIN no notifications so I'm thinking September at best for me.