I'm a little late on this, I just read your post.
All I can say is here we go again. (Claims vs Mineral rights)
It matters not, who's name is on BLM documents that claimed the original claims, as that name could be on the BLM records for generations, until the claims/mineral rights revert back to the BLM and are reclaimed.(goes back into the claims available pool in the BLM office)
What does matter, is who holds the "MINERAL RIGHTS" on those claims, the mineral right can be transferred by contracts over and over, and the original claimers will always show on BLM records. Until all mineral rights on claims are abandoned, That is not about to happen here at this time.
Searchlite has no doubt sold all or part their mineral rights to the acreage that they claimed, no need to have anyone reclaim, it is all contractual at this point (a transfer of mineral rights for value received).