And I can't wait to see it. It was worth the wait, and I am glad you stuck to your guns. They play on your emotions to make a sale, and it's a pretty twisted game to sell what they have, vs selling you what you want.
Appraisals are for insurance valuation, not for resale. Are you planning to resell it later? You're paying for brand with Tiffany, vs actual diamond quality. That comes with a premium both upfront at the register, and in value retention in resale. But diamonds and jewelry on their own just don't resell well. They are not investments.
Many of the vendors I'd point you to have a trade up policy, where you could trade the stone up later for larger and there's no real time limit, where Tiffany has a 5 year limit, as I understand it. Meaning you have up to 5 years to trade it up, and you have to spend X amount on the upgrade. Each of these might have different "requirements" as in, you have to upgrade say a color, or a clarity grade, but not so much value in price. Each has different requirements. But some have downgraded in size to get higher color and clarity.
Several online vendors can produce very nice replica settings and all of them sell incredible diamonds, cut to rigorous quality standards. You could select your own, and they provide extensive documentation--UP FRONT--with images.
If you REALLY want the brand, stick with the brand. Just maybe find a different SA/store. I think you said NYC, there's several stores in NYC. And maybe don't give them the Cheat Sheet, just tell them you want stones in this range, and we can yay or nay them on our own.
If not, we can work on going a different direction to get the look of the brand, and not the drama of the brand. Brian Gavin Diamonds has a few Tiffany style settings (I have the tapered one), and there's also a few vendors that sell the Vatche U113 which is the closest one I've seen to the real thing--it fools the brand. Rumor has it that the designer used to produce settings for the brand, but it's never been verified. Depending which setting you want, we can find a stone from those vendors.