The requirement concerns qualifying employment with the organisation, and an independent contracting engagement is a different legal relationship even where the day-to-day work looked identical. Whether earlier periods can count turns on the specific facts and is a question for counsel, not something to assume while planning the transfer.
Describe the relationship, not the work
The natural instinct is to explain how essential the person was and how long they had been involved. What the assessment needs is who employed them, who directed the work, whose equipment and systems were used, and how they were paid. Two people doing the same tasks can be in quite different positions here.
Provide that detail for each phase and let the analysis follow from it. There is a further reason the distinction matters in practice. Where the earlier arrangement ran through the person's own company or through an intermediary, the counterparty on the paperwork is that company rather than the individual, and the documents will show invoices rather than payroll.
That is not a defect to be explained away; it is simply what a contracting relationship looks like, and it is better presented plainly than characterised as employment in all but name. Give counsel the agreements, the invoices and the tax treatment for the earlier phase and the employment contract and payroll for the later one, and let the assessment proceed from documents rather than from emphasis.