You'll be fine. just give the green day marker 5 a little bit of a berth and then honor the channel markers all the way up the river. doesn't matter if you're entering from the east or west, you'll have at least 7' at mlw so you should be good. It doesn't get too thin or narrow until you get up above the bascule bridge closer to Mystic Seaport.
Oh, and if you do touch down there by Morgan Point, it's muck.
the J120 I sail on draws 7' and we have no issues near the entrance to the river. The biggest problem spot I've seen is the curve in the river between N22 and N24. Lots of boats run aground there if you take the turn too wide.
I draw 10 foot and am on the river at Mystic Shipyard. At 6.5 feet you should be fine. A few notes, some of which you have already heard:
If you knew the area, there is lots of opportunity to cut into the channel before Mouse Island, but given the circumstances I would play it safe and come in from G1.
Stay east of G1 at the entrance to the channel way out in the sound. There is a relatively shallow rock to its west.
Stay inside the markers from G1 down to the day marker. The area to the east of this is all rock ledge. To the west towards Mouse Island is better water, but play it safe and stay in the channel.
As you approach the Day Marker at the bottom of the river right off of the point in Noank, there is a ledge that runs on a SW to NE axis with the day marker right on the middle of it. The ledge extends half way out in the channel south west of the day marker and about 1/3rd of the way out into the channel north east of the day marker. At low tide, I would say that ledge is about 8 to 9 feet down so you should be fine, but if you want to play it safe then just make a wide turn around the day marker and don't cut it close.
To the east of the day marker, the east side of the channel up into the river shoals up a bit from mud that gets pushed down off the mooring field. Stay a boat length or so inside the eastern side of the channel.
Stay inside the channel on the way up the river.
As noted above, the curve of the river from N22 to N24 shoals up badly. The channel curves away from Noank Village Boat Yard over towards Mason's island before it turns north again. Starting at N22, it has shoaled up with mud from the main mooring field so the south side of the bend is relatively shallow. Stay close to the green markers and the northern small mooring field as you transit this bend. and you should be fine.
Turning north again, if you stay in the channel you should be fine all the way up the river.