Just this bit:
... during the period of time I am in the employ of the Company (including during my off-duty hours), ...
Is enough for me to recommend "hell no" as the answer. Unless they're compensating you sufficiently for working 24 hours a day, 7 days a week. If you sign this, I hope you're asking for something like a million dollar per year salary (you have to keep opportunity cost in mind as well).