Regulation of chromatin structure
"Are these modifications the primary regulation mechanism for chromatin structure?" 

It depends on how you define primary, we might currently think of histone modifications as primary because other regulatory mechanisms have not yet been well studied. Something else you can think of are the various regulatory proteins that interact with histone marks to modify chromatin. 

I don't think you should imagine chromatin as assuming "the most compact structure possible until histone modifications are made to enable transcription" but rather histone modifications being a dynamic process with various transcription factors (a class of proteins) coming in and adding/removing histone marks as well as 'remodeling chromatin' (adding/removing nucleosomes)

As a sidenote, I don't believe much is known about the tertiary stage you initially mentioned so maybe that could play a huge role in the regulatory mechanisms of chromatin structure, it has just not been well explored.