Those sherds do not look modern to me, they are not glazed and appear to be thin in thickness, and the surface imprint looks more like historic or prehistoric Indian pottery to me. If I were you I'd probe around the area and see if I could find some more vessels, good luck, you could be on to something amazing !
If I may. I have a pot that was broken and gifted to me and is in about 95% complete. I used the cheap white Elmers glue to put it back together. I used those cheap plastic clamps to hold the pieces together while they dried. It was a fun project and like putting a puzzle together.
Cool find, not modern. Could be associated with a burial, but not a burial. There's not that much evidence of urn burials in NA, it's more Central America. There have been pots found containing bones, but they appear to have been placed in them long after the original burial. Always a few exceptions though. If you found a pot, that's a good indication of a village site, so probably more artifacts around.
I agree with everyone, looks NA to me and not modern. I didn't know that about the infant burials that "back of the boat" spoke of and it's very interesting and makes perfect sense. It's an awesome find and yes you need to go do more searches, no telling what you will find in that spot.