Ok. I used to own a music school and music retail store.
You need to think this way: how much did
they pay for it? The minimum discount for instruments for any dealer is 50% but most dealers get a lot more because they buy large quantities.
Let me give you an example. That Yamaha you were talking about. It retails at around $28,000 you said. I am assuming they got it at 50/20% at least. That means they got 50% off the retail, plus an additional 20% off of what is left. That means the piano you were looking at cost the dealer $11,800. Maybe less... I've seen manufacturers offer instruments as low as 50/40% but maybe not Yamaha.
So if the dealer payed about $11,000 for it, they could easily afford to sell it to you for about $20,000, and still make a good chunk of money. The question is if they are willing to do that.
It is really a question of "who is more desperate"... Are they desperate to sell it and get some cash flow, is the sales person desperate to sell it and make a good commission, or are you desperate to buy it?
Also, if they are not going to go down in price so much, you can always ask for other things: free tunnings for five years

, free delivery, store discount for buying sheet music, and so on.
Good luck