My question involves labor and employment law for the state of: NJ

Howdy. I find myself about 4 months into a 12 month consultant assignment. I have a so-titled Consulting Engagement Agreement with an agency that pays me on a W2 to work at another company, and stipulates that I provide two weeks' notice to terminate the contract without cause (resign). The full text of the Termination section is included below.

The thing is that I have just accepted an outside full time offer that was impossible to refuse, but am uncomfortable letting go of my current post until everything is said and done (pre-employment screening). I do not anticipate any issues, but goodness knows what can happen. I would thus prefer to give notice as late as possible, in the unlikely event that something does go south. I am willing to pay for this 'insurance' (new offer is more than worth it), but I want some opinions on whether I am opening myself up to significant risk, quantifiable beyond a few thousand dollars.

With regard to my timelines: as of today (12/28), I am already too late to give a full two weeks' notice. I will not be fully comfortable giving notice until I fill out the I9 for the new employer, which, in about a week, would put me at just 2 days' notice. If, however, the new opportunity falls through, I myself will not be falling without a safety net.

Etiquette and politeness aside, can I give this little notice without fear of further action by the agency to recoup XYZ? I greatly appreciate any feedback or alternative suggestions (within the parameters set forth above, of course) that will keep me away from any action by the agency. Not to say that it will get to this point, but my preference would be to pay rather than litigate/arbitrate/mediate.

Section 3.01 Termination of Assignment.
The Consultant’s Assignment by the Company may be terminated under the following conditions:

A. Termination for Good Cause by the Company. The Company may terminate the Consultant's Assignment hereunder at any time for "Good Cause" and without liability except as specifically provided for herein. For purposes of this Agreement, the term "Good Cause" shall mean Consultant’s (a) failure to perform his duties as described by the Company and client hereunder (other than any such failure resulting from Consultant’s physical or mental illness) up to the Company’s standards of performance or the standards set by the client, (b) violation of any material provision of this Agreement or any other agreement with the Company, including but not limited to the rules and procedures contained in the Company Code of Conduct, Consultant manual or handbook, rules and procedures or any other Company policy, (c) conviction of a felony or any crime or improper act that could subject the Company to liability, (d) commission of an act of dishonesty materially harmful to the Company, or (e) willful violation of any law prohibiting or regulating the use or distribution of illegal drugs or other controlled substances. The Consultant shall not receive any accrued but unused or unpaid benefits if such termination is for Good Cause.

B. Termination Without Cause by the Company. The Company may terminate the Consultant’s Assignment hereunder at any time without cause ("Without Cause"). Termination Without Cause is a termination by the Company for any reason other than Good Cause as outlined above. Upon termination Without Cause by the Company, the Consultant is entitled to receive from the Company any accrued but unpaid salary as well as receive from the Company any unreimbursed expenses or other accrued yet unused or unpaid benefits owed as of the date of termination.

C. Voluntary Resignation by Consultant. Consultant may effect a voluntary resignation ("Resignation") at any time upon two (2) weeks, i.e., 10 working days, written notice to the Company of such intention of Resignation. The Resignation shall be effective as of the date set forth in such written notice by Consultant or any such earlier date at the discretion of the Company.