I have moved two tables, myself, this past year. The first table, my son and I completely disassembled as we had a tight fit putting it into a Uhaul trailer alongside the furniture and Gold Crown light we already had in there.
The second table I just moved two weeks...I had lots of excess space in the Uhaul this time, but didn't have my son helping me and was relying on the seller to help me disassemble and load the Diamond Professional. I left the slate support frame-bed assembled and tied it to the side of the Uhaul. Upon further examination when getting back home early the next morning, I realized that one of the screw-in insert connectors was missing and the frame was attached in that corner with a long wood screw. I also found another wood insert was rather loose. The seller was the original owner but had the table moved once before: a billiards company disassembled it in Arizona, the moving company shipped it to New Mexico, then a second billiards company assembled the table. I assume a couple pieces got lost in all that and the assembling billiards company took some shortcuts. I ended up doweling, drilling, and putting new screw-in inserts back into the frame, so it is structurally as intended. In hindsight, I should have disassembled the frame before loading it into the Uhaul. I would have caught the small problems right off...as it was, I was more intent on inspecting the outwardly visible portions of the table such as the rails, aprons, slate, etc. I think with an older table like an Anniversary, there is a greater likelihood something has been repaired over the years and a full disassembly would allow better inspection. That said, it sounds like you are not going to be present during the disassembly? I'd suggest getting someone involved on both ends, if possible, that is familiar with Anniversary tables. They are gorgeous and beyond my price range...I certainly would not want anything damaged during the move and would want to get anything that is already a substandard repair done correctly as your table is being setup at its new home.