I did a very similar mod. For the gap between the top of the mattress and the headboard I used pool noodles. I stacked them 2 high and 2 deep, secured them together with tape, and cut them easily to length with a large kitchen knife. (use as many noodles youneed to match the height of your mattress). When I make the bed I use regular queen sheets and put the fitted sheet around the mattress and the noodles. It is barely noticeable.
With a past mattress I did the same thing but laid a mattress pad over the noodless and the mattress before making the bed.