The reason you don't like the flush is that it isn't starting with enough water in the bowl. Amazing what a difference it makes. There are a lot of posts on here about this issue, usually because the refill isn't adjusted properly. (Yours is, so that's not the issue here.) These toilets are actually finely-tuned machines and need the right amount of water to start with.
Now, on to your problem. Three possibilities: the toilet isn't level front-to-back, something is wicking or sucking the water from the bowl, or the top bend (where the weir is) has a defect that is causing water to run out below the proper level of the weir. I suppose you could scope it for a defect, but if you're not happy with Toto customer service, I would just call them and tell them that you have eliminated everything about the installation which could have caused the problem, and therefore you believe the bowl to be defective and you want them to send you a new bowl under warranty -- unless they have another suggestion to check for. That will get their attention, and maybe some other suggestions we haven't made here.
Don't give up on the Drake. It's a great toilet. Try replacing with a new bowl (the tank sounds fine) under warranty. If the problem still exists, then it's something to do with the installation -- like I said, level or suction being most likely. The latter less likely because the problem happens consistently every time. You also might just try loosening the closet bolts and shimming the toilet in the rear a bit, more forward, then seeing how it works. You still might need a new bowl, but if you can get it reliably-full to start, you'll have a sense of how it should be working. (If that does solve the problem, you will need to reset the toilet with a new wax ring, because you will probably break the seal when you move the toilet.)