I'm 99.999% positive you have Biot, Nev.
I got my big bottle out and the rubber gloves and the floor cleaner and green scrubby things and I have cleaned it so I can see inside.

What you are calling the pontil mark is really not quite right, I don't think.

The circle of "bitty" glass is far too big. And I strongly suspect, from the
flat topped dome inside the hollow that it might have been a broken pontil mark that was subsequently put in a mould and blown again.
The bottle base flares out. The only way the huge hollow, with that ring half way up inside it and the flat top (or bottom) right in the centre, could have been done is in a mould.
So, a broken pontil scar would have stretched into the big ring we see. This would mean they had worked the thing from both ends.
I can only find one image online of the big stoppered bottle with the flared base. But it's on an auction site well-known for imaginative prices and for following you around for months if you ever click on it. So I haven't clicked on or linked to it.

The image is of a collection of pale blue Biot pieces.