Their platform was a multifaceted approach. They did discuss tiered parking prices for commuters, one way streets with diagonal parking, a garage, subsidizing Uber, parking apps, possibly using the Zabriskie lot, employee parking, etc. The council discussed the parking rates in October and November, before voting on it. I don’t believe any member of the public complained about the price being tiered higher as you got closer to the train. The Financial Advisory Committee suggested raising the commuter passes as well as the meters, especially the meters on the streets closer to the train station (75 cents and hour was suggested). The council chose to keep the meters the same, except to lower 60 meters at Cottage to 25 cents an hour for CBD employee parking. These were both done to try to entice more people to use the Cottage Street lot, which remains mostly empty all day.
When the previous council was planning a garage, they said the garage would be mostly for patrons of the CBD. They said commuter parking would be on the upper levels.

Say the garage was built at Hudson. If 2 cars started from the same location, one drove directly to the Cottage lot, parked, & walked to the train platform. The other car drove directly to a garage at Hudson Street, drove round and round to the 3rd level, parked, came down to street level, and walked to the train platform- my guess is that the timing would be pretty much the same.