Strange slipping issue..

Did you end up checking the flex plate bolts where they thread into the converter like Threewood suggested? It is difficult to tell in the video but does sound like something rubbing or scraping when flex is induced under heavy load. That needs to be ruled out first. Also, I did have two completely different 727 transmissions in a 74 Newport that, at the time, I thought were not slipping. Under harder acceleration it would start to shake or vibrate and then sounded like a hollow grinding noise from the middle of the car. That noise is something I have never again heard duplicated in any other car I owned, regardless of what went wrong. After some brake torque testing while stopped in drive, similar to the video shown for your problem, it was determined that the transmission WAS in fact slipping. The rpm was going higher than it should according to the specs in the service manual (car was completely stock so specs were valid). At no time did my car ever slip badly enough to be obvious to me until right before it completely gave up and had no forward motion at all and would just rev up like it was neutral. Teardown and rebuild showed absolutely no damaged hard parts but I did find the forward clutch pack (rear position with the input shaft attached to it) was completely burned out, like no clutch material left on the discs at all. The steel plates and even the clutch drum was discolored from heat caused by all the slippage. After rebuild, the rpm was normal during brake torque testing and the noise was completely gone. Definitely need to rule out anything that could be rubbing first, and also check the actual rpm it gets up to when holding it against the brakes.
Good luck. Bob.