@drbond - a spindle weight goes against the Rega philosophy 180 degrees. Roy is against weight and it may impact the TT PSU which is designed to move a very lightweight platter. You don't need that to eliminate the reverberation you are hearing - Isolation/vibration control for sure will do that, but verify that whatever you use is effective with something as light as the P8 at only 10 pounds.
The only thing that worked for me was the Townshend seismic platform with the smallest possible pods (AA), which eliminates the worry of where to put the podiums or hockey pucks (which I use under my phono and amp) - not individual podiums. New turntable mat - maybe - I tested a few because my Rega mat kept lifting up occasionally when changing records, but I didn't hear any improvement and most still lifted up, so I just put a couple very small pieces of double sided scotch tape under the mat on top of the platter. Plus the black mat on the Rega table is a classic.
SME would definitely be a step up, especially with their top arm, but it will be 4-8 times the cost of the P8. Good news is that if you unload the P8 you will get a good % of your expenditure back. I'd be interested to hear your impression if you get the SME keeping the cartridge and phono stage the same. If you change multiple things at one time it will be hard to tell what improvement was due to each change. I've had that happen. Oh well, there are bigger problems in the world.