Got no real experience with this. Like JL, I was diagnosed while employed, and my employer (who was also my health insurer!) went through the whole thing with me & were very supportive.
Your previous experience could have been a one off (is there not a law in the USA to prevent discrimination on the grounds of disability?), and maybe these folks will be a bit more supportive, especially as you are not going to have any specific special needs. At least this way, if you do need time off for a relapse or doc visit, they will understand. It just feels a bit off to actively withhold the information - your health insurer will know....Maybe just stress how well you are currently - a letter from your neuro might help.
I don't really know though - just my instinct, please go with your own and make sure of your legal standing before you do anything...
All the best