Google "hand embroidery fill stitches" and lots of ideas come up.

Donna

One long straight stitch would be loose and messy.

You could do long straight stitches, but with a 4 inch span you'd want to work something over them to hold them down. There's a technique called vermicelli that can be worked over a satin stitch background- it's often done in gold or other metal threads, but I don't see why you couldn't do it with plain threads. Lattice work could also do very well as a filling for such a large area.

This is new crown in my project 1 inch.

http://embroideryviet.com/top-10-must-know-hand-embroidery-stitches/

I don't know "types" of stitchery. I'm mostly self taught, but when filling in an area, I usually outline a shape, then fill in by doing about a 1/2 inch stitch, then splitting it in half like the photo above, repeating over and over. Usually starting from the outer outline and working towards the center. Hope this makes sense.