I kind of look at it this way - if you have to immediately grab a pillow to make the unit usable, then you picked the wrong chair. Having said that, yes, a pillow may help, but also its a function of height and personal preference. If that recliner doesn't work, then there are another fourteen or so nearby to try out as well.

Air and Space Museum on the Mall is being renovated so it has sections closed. Where you REALLY want to go is the Udvar-Hazy unit at Dulles Airport - because that one blows away the downtown one for aviation buffs. Much larger, more airplanes....a lot more.

https://airandspace.si.edu/udvar-hazy-center