Safety factors
I've seen plenty of cars built that way and they pass tech. The front bars are tied to the cage but it is low. The halo shouldn't be a problem. The only thing I see from the pics are it needs a dash bar running from the front cage bars across to each other to tie them together.
Yeah if the bars went through the dash and the front extension bars were mounted higher it would probably be stronger but it may still pass a certification provided it has the dash bar.
But I would really have an NHRA certified chassis inspector check it first because if the cage isn't thick enough it will never pass. Then you'll be redoing the whole thing.