Hey b, i will try again, pictures will realy help out 
, But as you said @watchthebear wrote:
escape wheel has the “points” curved upward
, or @watchthebear wrote:
the ends of the wheel are turned upward, and there are more than on a regular escape wheel
would almost sound like a “verge” escapement, but then again when you said, @watchthebear wrote:
There is a notch in the balance shaft where the pointed parts of the wheel must strike the shaft.
sounds to me like a “cylinder” escapement. which when you said, @watchthebear wrote:
where the escape wheel also serves as the pallet?
starts to make even more sense, but when you said, @watchthebear wrote:
(like the stylized lotus flower) and connect directly w/ the balance
😯 I had no clue, BUT then again that is usually the case, so in my limited knowledge and the desire to help others out, my best guess would be a cylinder escapement. I found a small book on escapements by, F.J.Britton called “the escapements” their action, construction and proportion. very inexpensive yet yields good information, I am sure there are many other books on escapements and the theory behind each and they would be good for any of us to get ahold of. 
Keep on keepin on, William