It entails replacing the steering assembly and sensors, which get dirty and noisy. Not cheap but less bad than replacing the computer and discovery the problem remains. One test is if the vibration goes away for a bit if you fully turn the wheel stop-to-stop with the car 'off'. This is just a 'wipe the wipers' effort that sometimes gives temporary relief. Bob Wilson
I do not believe it is possible to "reprogram" any of the Classic ECUs. Is your "shop" a Toyota dealer's service dept? If not, I'd be concerned about whether your mechanic has good info available to him/her.
The only way to solve the problem permanently is to replace the steering rack. If you order a new steering rack from toyota it will come with a new computer too. I cost around USD$ 960 when I order it last year from internet, then I bring them to my dealer to replace it. If I order the rack directly from dealer, it cost me around CAD$2000 just for the parts.