This response is based on the information provided.  We suggest you discuss with your contracting team, program manager and/or legal department as appropriate.

Choosing contract type should be based on an assessment of cost risk based on history/research, etc.  The CPFF Term form calls for a specified level of effort for a stated period of time.

The FAR already has the contract structure you describe - Labor Hour (LH)/Time & Materials (T&M).  In this arrangement, you have an agreed-to burdened labor rate to which you add a negotiated profit (10% or some other rate reflecting the lower risk to the contractor in this arrangement).  That is what you describe in your scenario.

The scenario also encourages the contractor to perform as many hours as possible in executing the task because each hour brings more fee.  The CPFF anticipates there is slightly less motivation to spend every hour, because the contractor gets the full fee yet returns unused hours/dollars.  The contractor might be motivated to finish quickly as it can pursue other jobs, hopefully FFP contracts, with higher returns on investment.

So, to do what your team describes, create a LH contract.  You will need to write a Determination and Findings (D&F).  To do what your team describes as a cost contract is, in our opinion, an illegal Cost Plus Percentage of Cost contract [prohibited per FAR 16.102(c)].  You cannot use any contract type not expressly described in FAR part 16 unless you obtain a deviation (FAR 16.102(b).