It's been about 6 years since I was a totally independent contractor, but I did that for more than 20 years. During those times if I was working for an extended time with a single company it was usually the company's own HR that would scream and howl if someone was asked to work "off-the-clock" who wasn't a salaried employee.

The laws are different state-to-state, but generally speaking a company (and you) are at risk of losing your independent contractor status in the eyes of the IRS. And what the IRS decides is really all that matters. Losing independent contractor status means in essence that the IRS deems you to have been a salaried employee of the company and thus the company is going to be hit with back taxes and late penalties for not paying your quarterlies, etc. It causes a real mess and likely will lead to termination.

I've seen the two sides of this both as a contractor and as an employee of a large accounting firm. I recommend that you do some research at IRS.gov and review the contractor rules. The IRS doesn't really care about contracts if their guidelines determine that you are really an "employee" even if you are working through a third-party. And in their eyes the employer setting your hours is one critical sign that you are not an "independent" contractor.

The ice is very thin beneath your feet so please get some professional advice (i.e., CPA or attorney specializing in labor law).