You are allowed to tow on the Parkway. there are a couple of low bridges but they are only low in the right shoulder and right hand lane. If you stay at least one lane from the right you should be good.
You might not have EZ Pass but if you do it makes it muuuch easier. Try to avid it during the commute. Traffic is horrible. I did it many times because it was the best game in town for us.
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