I know pathologists who have had no extraordinary issues with TSA when carrying boxes of slides to/from Sloan-Kettering or M.D. Anderson. The boxes of slides are less problematic for clearing screening than a wheeled cabin trolley chock full of a dense stack of medical journals with high-gloss, coated paper.

Your pathology lab should have appropriate packing material to safely transport slides and perhaps they'd give you some. [It's rather within the range of ordinary for pathologists to send slides for additional consultation from one medical center to another, and even those containers most frequently clear the TSA just fine -- even as telemedicine is increasingly part of the picture some pathology lab habits just don't change that much.]