This sounds like the exact problem I had to tame awhile ago. Nothing to do with external stores or massive overspeed as I can get this to happen at less than 800 knots at much lower altitude so that mach is only around 1.15 or so. Guessing my system was giving it too much performance as I had to enable v-sync on the newer drivers/cards in BMS to tame that mess. Another odd bit about this was with the newer drivers/cards and v-sync off I could only duplicate this when flying over water. Flying over the peninsula removed the problem.
100% duplicatable as many times as I wanted to. I posted on this a few times and made videos about it. Don’t assume people are messing up and not understanding LCOs as that isn’t necessarily the case in BMS and hasn’t been for a LONG time as this problem is long in the tooth.
Here is the link to my initial posting under another poster covering this subject in detail.
https://www.benchmarksims.org/forum/showthread.php?14469-Aircraft-shakes-along-roll-axes-when-traveling-above-Mach&highlight=funky