I did already know about the residence permit but that is putting the cart in front of the horse. Logically, if I am able to receive and use documentation prior to my graduation in getting a Z visa then I can do so soon; landing with a Z visa with 2 weeks to spare should be ample time to get my RP before courses begin. Don't you agree?

My point is, Justin, you wanna be legal. Fair enough. But the school has its own agenda. Your presumption that two weeks is enough to get you your RP needn't be agreed by them. They really needn't care you have made a life-changing decision. You came from afar to fulfill their requirement for an FT, as they see it. You can't get an RP on your behalf. They need to do it for you. They have all the aces. They needn't say anything about when you will get your RP after you arrive, but they must get it within 30 days of your landing. They can choose to delay as long as they feel necessary to check out your teaching.
BTW, have you signed a contract with them online, and have they stamped it, or have you merely used their invitation letter, or will you be sent it, and subsequently use it, to get your Z visa? If no countersigned contract, you're wide open to bait and switch tactics. Now, after you've arrived, there will be other foreigners there, and what will you do if the university bullshits re the RP to you and the others while asking you to teach? The university will say, no problem, trust them. By doing so, they can check you out first, while you're teaching illegally, and dispense with you without any penalty or wasting money on obtaining an RP for you, as they choose, should they be dissatisfied with your teaching. Maybe the other FT's will agree, but you won't, on account of your principles. I reckon if you take up the 'legal' issue with them, they'll be dissatisfied with you, and deem you a troublemaker. A bad start.
Now, let's contrast another scenario, you arrive on a 90 day tourist visa. In the event of being driven away, you've the time with your foot on mainland, don't forget, to seek another job. You're here, a great plus for a potential employer! Some employers are desperate, take a job at a state institution, you'll be okay, even if your teaching is pretty bad. More options. Only thing is, you'll have to go outside mainland to change the tourist visa to a Z. Most FT's do an HK visa run to do so.
Either scenario involves illegality, but I think the second one is better for you, as there are more options, coz you're here, and immediately available country- wide for a longer period of time. An employer won't delay more than about 25 days in deciding your fate. If he delays too long, it will be hard for him to replace you - outwwith the recruiting season. However, do as you please! Don't forget, you're the one that stressed teaching legally in the first place. That's why I put the cart before the horse, and posted what I did. Good luck, whatever way you decide to play it, but beware of bait and switch!