If you get the overspeed warning, then you're going too fast for the FDE design. So you could double the thrust for the default 737 for example, and it would go faster than the design of around M0.8 - but it would then be outside the performance envelope of the FDE which is where the wobble comes from.
This is from the aircraft.cfg my 777 FD:
[Reference Speeds]
flaps_up_stall_speed= 138.0
full_flaps_stall_speed= 110.4
cruise_speed= 485.0
max_indicated_speed=330.0
max_mach=0.87
You can adjust both of the bottom two lines to affect the overspeed warning, but I think you'll have a major job on your hands to stop the wobble because you'll have to modify much more within the FD.
Moral of the story: fly within the flight envelope of the plane you're flying! Or construct your own FD so that you can get it to perform how you want.