I quite like that bit that flops down.
It makes your hair style look less contrived.
Although it may prove irresistible to someone wanting to sweep it off your forehead!
You could try using a quick blast with a hairdryer on a low heat or spritzing it with water, popping in a haircomb/slide and leaving it to dry.
Or, you can use the hair net that the piece came (usually) wrapped in by putting it over your hair and again use a dryer or letting it dry naturally. You can 'tweak' it to the exact shape you want through the net using a 'picking' comb.

NB, don't forget to take it out before leaving the house, as I have done on many an occasion!

I think you're doing a GREAT job and will have this whole thing nailed in no time.
Like someone else has suggested, I think you should have a go at using Oil Resistant White Glue (ORWG) on the front.