You have beautiful strands. Regal strands, really. Having willingly provided additional photos and supporting certification, you've also indicated to being a collector, not necessarily a salesperson. Whatever their origin, your reverence for pearls is outstanding.
Glancing at the new images, some are consistent (but not exclusive) with pearls from P. radiata, namely luster and color. The shapes are typical of most species.
The sizes are a concern. 5mm to 11mm graduation is not typical. It's rare, especially in multiple strands.
Of the many gulf pearl strands I've seen, most are graduated 2mm to 7mm on average. Market value of single strands in that size range from one to six thousand dollars. Strands more than double that size could fetch four to six times more value. Add multiple strands you'd be looking at six figures without considering the metal, faceted gems and craftsmanship.
I understand in informal settings, such as forums like this, many are reluctant to specify prices paid or offered, but a to discerning collector a "decent price" is a widely subjective term. It can mean dirt cheap or it can mean near to the expected price at auction. Two markedly different things. Appraisal is intended to narrow or eliminate variables, not to confuse or compound them.
Despite my apprehensions, it's fair to suggest lab certification is a reasonable step in determining the origin and value of natural pearls. However, it only adds one or two points supporting authenticity. Anyone would be wise to consider it's limitations. Without impeccable provenance, the value of any questionable object is radically decreased. As in archaeology, without proper documentation and record keeping, the greatest part of any value is lost once it's removed from the site.
From a scientific standpoint drilled pearls are destroyed pearls for the most part.
My only advice would be an abundance of caution and a broadened education. Much of which you'll find from the many talented contributors here.