It is only a slight over-simplification to say that one key difference between an employee and a contractor is that an employee gets paid by time and a contractor by output. There are obvious exceptions, such as piece-rate or commission-based employees on the one hand, and contractors who sell their services by volume rather than product on the other, but so far as wild generalisations go, that one is pretty tame.
So if you are trying to show that your PSC contractor would not be your employee even if you removed the PSC, paying his company a flat rate per month, just like a salary, is a really poor start. If you use external help to have your house painted or your IT system upgraded or your social media presence revamped, for example, you would not sign a contract which says (by implication) take as long as you like and just send us the same bill each month. Instead you would want to pay for results, or half in advance and the rest on achievement of defined milestones. Even where the services are supplied and billed on a timed basis, it is best to relate the fee payable to actual time worked within the billing period, not the billing period itself. In other words, not a flat monthly figure but a number which varies each month with the number of working days in it and absences by way of leave, illness or other commitment of the contractor (unless a substitute is provided).
By way of further separation from your salaried staff, make it a contractual condition that your consultant’s fees are payable only on production of suitable evidence of the work being done. Ask the PSC to submit timesheets, ideally of its design rather than yours and not looking anything like those you might use for any of your own employees.
Much preferable, obviously, is to bill on results. This will require a detailed assessment of the steps in the project at its outset. This sits nicely with the desirability of the agreement looking like a commercial rather than employment contract. It helps focus on the what is to be done, not the how, or the by whom. That also helps show that the PSC is genuinely in business on its own account because it (through its individual contractor) must then apply its mind to the resources it needs to achieve each milestone. It can make a profit or loss (or merely scupper its own cash flow) by particularly skilled or unskilled exercise of its professional judgement as to what those steps will be, how long each will take and how much it will cost.
As a related cosmetic detail, it will be preferable for the PSC’s invoices to be processed in Accounts along with all your other supplier bills, and not in HR or anywhere near the payroll process.