Ok I see thats not to bad. Now you have an option at this point it's up to you whether you do it or not but I would cut out all them cross supports, they are only there for the dome installation, if your filler coat on the outside of the dome is strong enough it should withstand you pulling them out, use a pair of wire snips to snip them all out and remove as much of that inner ring also, the reason for this is simple, you will need to get a helmet liner in there and padding and these cross supports will limit what you can use. once that inner part of the dome has been fiber glassed after they are romoved it will be strong enough to support it's self. also it will start to get lumpy with layers of fiber glass going over them supports and space inside these helmets is at a premium!
Like I say this is totaly your choice if you remove them or not but in the long run it will create space and you will get a better, harder finish with the fiber glass,
I would add two layers on the dome, srtps going one way, the the second layer of strips going the other.
the cheeks you can cut them to shape on the manddibles and add one good layer. try to visualise tyour goal and prepair everything first, 
