Maybe a Merlin?
Or maybe a Tern or Gull?
Still thinking a Gull , maybe an immature greater black backed. Gulls fly up the Kennebasis quite often, all the way up to Penobsquis where they use fish guts for compost.
A Jaeger or other seabird so far inland along the east coast would be exceptional. What's the likelihood that a single person would have two such sightings widely separated in time and distance?
Now I'm not doubting the sightings but I'd suggest that, if both sightings are the same species, it's highly likely that it's a fairly common species.
Petrels are out simply because of size. Likewise Terns are out on colour and size.
I'd also suggest that given the time of year there's a strong possibility that you should be looking at immature and sub-adult birds.
You haven't mentioned anything about it's flight. Did it soar or glide? Did it flap its wings? Fast, slow, deep, shallow?
Any additional information might be helpful.
The sketch shows a dark front end/neck region with dark underwings and that is inconsistent with the majority of birds that one might find in this region. I'm sure there must be others but only two in your general size range that come to mind: female Surf Scoter and 1st year Great Cormorant.
I strongly suspect that the apparent dark wings and underbody were at least partly the result of viewing the birds against the bright sky.
It's a nice little mystery. I look forward to other opinions.
I think that we all look for those "fingers" and sort of expect that they will always show but I know that I've been fooled a few times when the primaries were held tight, similar to your last pictures.
I've burned a lot of gas turning back to check quick glimpses and almost always (if the bird was still around) it turned out to be a familiar species.
Your suggestion of Osprey is a reasonable fit.
I'd also agree that a backlit Osprey would be a far more reasonable suggestion for a sighting in that area.