Here is a photo
of a NavAid located in the narrowest part of the Merrimack entrance buried by current/out going tide. I took this as I was puttering along at 1 kt past it in a sailboat under full power.
I strongly think it is a better option to put your boat in Beverly or Salem harbors. Aside with not having to deal with this if you miss time it, you can be in open sailing water within 5 minutes of leaving your mooring instead of the 30 or 40 minute crawl down the river to open water. I don't know where you'de be coming from on land, but Salem/Beverly are only 25 minutes or so from Newburyport on I-95/MA-114.