GaryH - I have never found the Longueuil parking lot to be completely full upon arrival (typically late afternoon, 4 to 5PM) however I have noticed on a couple of occasions the long-term portion of the lot is completely full. In that case I parked as close to possible in the day parking area, then returned the next morning to move my car to the long term area.
More recently I have been parking in the Complexe Desjardins indoor lot, which involves minimal driving on downtown streets - take highway 10 through the bridge construction into downtown, then right on Rene-Levesque, go five blocks then left on Jeanne Manse, then the parking entrance is on the right about 1/2 block down. As I recall, its $24 per night to park there, cheaper on weekends. I have never found the Complexe Desjardins parking lot to be completely full. Even when the Complexe Desjardins itself is closed (late night) there's a way to walk out of the lot up to the street. My favorite hotel is an easy walk away. Complexe Desjardins is convenient with stores, food court, ATMs, an IGA grocery and underground access to the Place-des-Arts metro station.