You are right to be concerned. The IRS and DOL use the pairing of the Plan Sponsor's EIN and Plan Number as a unique identifier. In your case, there was a final filing for the EIN/001 pairing. When the plan merged there was no reporting for that EIN/001 pairing, and starting to use that pairing now will cause confusion. I have seen this happen under different circumstances, a request was received for an explanation for the missing filings, and it was a pain to straighten out.
The spin-off plan is a new plan, has a new effective date, and has a distinct identity from the original plan EIN/001 and the parent's plan. The distinct identity to the agencies is EIN/002.