When a technician takes your car for at test drive, with the proper scanner hooked up, they should be able to see the signal for the convertor lock up to the solenoid in the transmission valve body. As the car is coming to a stop, they should see the signal disengage. This would verify that the ECM has the proper inputs and output for the convertor lockup to happen. If that is working then the problem is in the transmission. If the signal from the ECM is staying on while braking and coming to a stop then you have a wiring, connection, input sensor problem.
When trying to find info about your transmission, you need to know what transmission you have. The model of the transmission will be something like U250E, U341E, etc.. and is stamped on the transmission case by the engine. Find that and at least the transmission tech will be more willing to talk to you about the problem in more detail and you can see how they react, if they know what you are talking about. Here is some info to read as to who rebuilds, where they get their parts and info from for rebuilding and updating transmissions. If you read the pdf magazine, and it does have an article about the U341 Toyota transmission in it, toward the back of the magazine are list of suppliers and companies that specialize in transmission. They may be able to help you or point you the right direction. The second link is to find shops in your area that are up to date on info about your transmission or have access to the info to help figure out your problem. I think if you start reading the tech magazine, you will have a better understanding why people are telling you to replace the transmission. Mechanics are paid by flat rate hours and if the mechanic is not knowledgeable about your model of transmission, they are going to loose money on the job no matter what happens so you can understand why the dealer told you to replace it.http://www.automaticgearbox.biz/digest.pdfhttps://www.trnw.net/shop_finder.php
It is also odd that you have no error code from the ECM. Codes differ with the model of the transmission but convertor lockup problems are find around codes P0740 and up.