There are no fish in these rivers so stay at home!
OK, just kidding. There are several of us here on THT who live and boat in this very area.
The only public ramps in the area are the Ipswich town landing
and Perley's Marina in Rowley. There is a ramp on the Parker River in Newbury
but it is limited to town residents only (like me).
There are no restrictions to powerboats in the area, although there are several no wake zones that need to be adhered to.
Alternatively, you can access Plum Island Sound about 2 hours either side of high tide via the Plum Island River from the Merrimack River. You could launch from Salisbury State Park or Cashman Park in Newburyport. In a shallow draft boat like yours you may be able to stretch that to 2.5 hours either side of high tide.
The Ipswich River is navigable all the way up to the dam in the center of Ipswich, the Rowley River peters out just upstream from Perley's Marina off Warehouse Lane. The Parker River is tidal all the way upriver to the waterfalls at Central Street in Byfield, the low bridge at Middle Road in Byfield, near Governor Dummer Academy, is passable only by small skiffs. I have to stop at this point in my 20' center console.
All 3 rivers have an active herring/alewife run in the Spring which leads to great early season striped bass fishing. I have caught my first bass of the season on the Parker River on May 1st the past two seasons.
All 3 of these rivers experience 7-8' tide variations so local knowledge is definitely a good thing when traversing them for the first time. The Ipswich River, in particular, has several rocks that are exposed at low water and partially covered - ouch! - at mid-tide.* The Rowley and Parker are generally muddy so there is less worry about grounding.