Do I still file the 1099-NEC form even though the Payer's TIN doesn't match the 1099-MISC form?

Could you please give us more details on your situation and clarify why the forms should have matching TINs?  

A 1099NEC is for self employment.  You need to fill out Schedule C for it. You don't need to get or enter a 1099NEC or 1099Misc or 1099K.  Even if you got one you can enter all your income as Cash.  Only the total goes to schedule C.

You can enter 1099NEC or Self Employment Income into Online Deluxe but if you have any expenses you will have to upgrade to the Premium or use any of the Desktop CD/Download programs. All the Desktop programs have the same forms, so you can buy a lower version.  You just get more help and guidance in the higher versions.

How to enter income from Self Employment

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653

Is the 1099-NEC and the 1099-MISC for the same income??  Don't enter the same income twice.    It is okay to have different EIN numbers on different forms.