Disclaimer: IANAL
" all work necessary outside these times, including Saturday and Sunday, is already remunerated in the base salary."
That's actually not enforceable in most US states. Typically a base salary cannot cover work which is outside normal business hours if it's a consistent expectation that work will be performed outside normal business hours. Contracts are enforceable because both parties are given "due consideration", so that the terms are intended to be mutually beneficial. As written, what you described is basically saying "Do more work, do it outside typically expected times to perform work, and you're not getting anything more for doing this."
As an example of how this works, in a situation in which you will work consistently outside normal business hours but are a salaried employee, such as a manager supervising an overnight crew at a manufacturing facility, you will be awarded "Shift Differential Pay", which is a percentage or dollar amount differential above and beyond normal pay for someone of your position at the company as "due consideration" for agreeing to work outside normal business hours. This would be true for your overnight crew on the line as well, except that it's included in their hourly.
Being salaried does not automatically mean you are a slave to the company and their whims, and being overtime exempt does not mean you can be asked to consistently work outside normal business hours week after week without any additional compensation. Overtime is an occasional action, if you are being asked to work outside normal business hours as a standard operating practice, that's something else entirely.