It can be done.
I was at the track in my car on Tuesday*, and as I am as tall as you, the helmet does not fit well inside.
I moved my seat base forward and the back-rest further back than is truly comfortable. I was not driving to LA so I leaned forward and back till I found a place where my helmeted hear fit. In the link below you can see me while waiting, rolling and hanging my head in funny positions, to give my neck and back a rest.
*
Race School day two.