$2800 is the retail price for the transmission. You can buy it from 1sttoyotaparts.com for $2100 + shipping. I also found you a low mileage unit w/37k for $499 (or less if you made an offer) + $100 shipping
here.
1600 for labor sounds high, does the engine assembly need to be removed as well like it does on the 2GR-FE?
I would seriously consider ordering the low mileage unit and having an independent shop install it. The rest of the car still has a lot of life left in it.
How often did you change the transmission fluid previously? Usually these units are fairly reliable so I think it's a good candidate for an used unit.