First let me break this down a little for you. This is their cost. The parts involved excluding the torque converter and electrical switches run about 125.00 probably closer to 75. A rebuilt torque converter let's say 100 dollars probably 65. The electrical switches can run around 300. By the way these are after market parts. If they use Toyota they go up significantly. So to be safe let's say between 400 and 600 dollars in parts. Keep in mind that on transmission work some places consider the replacing the oil an extra cost. The drum they mentioned and the cable would be extra to this cost so you would have to check on those prices, but they are not that much and would probably fall within the 600 dollars total for parts.
Now you mentioned the differential. I am not sure why your rear end is involved in this. Are you sure you do not mean the transfer case? If you do mean the transfer case then it really depends on what they say needs to be replaced however my guess is there is nothing wrong with it if it only has 159,000 on it, but again the transmission should not have went out at 159,000 unless abused.
I have a 92, although I am looking for a standard in a 3rd generation, and the transfer case and transmission are one unit so it has to be removed and rebuilt with the transmission. Yours is not. So on mine they had to also rebuild the transfer case when they did the transmission. My bill for the transmission, transfer case, torque converter and all the electrical switches including towing was 2300.16 dollars including taxes.
I currently have under 3000 miles on it.
So yes I would say that they are shafting you. I used USA transmission locally. One thing you did not mention is the warranty time and miles. Long warranties can add a lot of money to a rebuild cost. I chose 6 months to get the cost down. If they are offering a lifetime or even a 3 year with 50,000 miles then the price that they gave might not be to far off as long warranties add a lot of cost. If this is the case then perhaps you can get them down significantly if you shorten the warranty, but 2500 including taxes out the door should be tops and a little lower is more in line. Tell them they need to get that price down to around 2000 and bicker with them like buying a new or used car.
Now about what to do. If you choose to allow them to continue and do the rebuild then you need make sure that price they give is out the door cost no matter what else they might have to replace, including fluid or internal electrical switches. On mine they were all replaced and they are expensive.
Now if you choose not to let them rebuild the transmission I would rent a tow dolly from Home depot or some rental place and go pick this thing up with everything tore down. That means you will now have 385 dollars in the transmission inspection. I would then find someone who would agree to put in a used transmission that I would bring to them or price around and see what it would cost to have that one rebuilt as well as replaced since it is already out. Keep in mind this might not work for you.
Now some information for future reference. NEVER, and I mean NEVER allow a transmission shop to drop a transmission to give an estimate unless they will do it for free. It is unnecessary. This is not their first rodeo and they know all the parts needed (they come in a kit and they usually never use them all) and they can give an estimate on a full rebuild without removing it. On mine they did not remove it to give me an estimate. I hope this helps.