Keep in mind the R/T and GT have different residuals, so just beacuse you pay X for an R/T doesn't mean his holds the same value, which is important in a lease.
I agree, put as little down as possible and do not give them any more than you have to. While you can use the positive equity at trade in time, you do not get the positive equity in an accident or insurance payout, so keep as much money in your pocket as you can.
$435 is NOT a bad payment, especially with taxes included, for what you are getting. Is there wiggle room to save a little more, probably. But if you are comfortable with the payment, happy with the interaction at the dealer and what you are getting, then do it. Peace of mind is more important than $8 a month. If you want to bottom out the pricing as much as possible, shop around, and see if there is a better deal to be had.
As far as "Getting NOTHING for $3000 down and $X per month", what you got was a much cheaper payment than buying for 5 or 6 years worth of payments without worry of any repairs or maintenance (if you negotiate your maintenance in, which you always should with a lease). Yea, you turn it in, and you probably should put $3000 down anyway, but that $400 payment for 3 years would have been $800 for 5-6 years had you bought it out. Thats the beauty of leasing.
Nevermind the fact that if you end up with negative equity, you can wash your hands of it and never worry about it. Whereas if you bought it, and it was in the red, you have to eat that. We had a 2014 Cadillac ATS for my wife, our buyout was $27k-ish after 3 years. It was valued at under $20k. If we had bought it, we would have been screwed at that mark. Instead, we handed them the keys, got a new CTS, and walked out without losing a penny. Leasing works....but only if you want new cars all the time, and don't mind having a payment forever.