Since both employers used the same payroll service and they used the same ein you cannot fix this on the tax return which is why the excess was not recognized automatically.  Talk to the payroll company and see if one or both of the EIN numbers can be corrected.  If they cannot (or will not)  then your ONLY option is to file file a claim for refund using Form 843, Claim for Refund and Request for Abatement.

Since this is on a 1040X where you must mail in the return with the actual  W-2 forms as proof ... to get the TT program to work correctly simply change one of the EIN numbers on one of the W-2 forms since it will not matter ... just change the last number so it looks like 2 employers to the program  to generate the Sch 3.

The same EIN indicates it was ONE employer, even if they did reorganize.  I think your employer needs to correct what seems like their mistake.