The limitation was actually not to exceed 300kts with the speedbrakes extended, with a warning that speeds in excess of 320 could cause severe vibration and damage.
This limitation should have been cleared from all fleets by having the elevator tabs “stiffened” IAW SB 737-55A1080. It was recommended to be done within 2 years of Sep 2004. You can check this visually on a walkaround by counting the number of hinges on each elevator tab, the modified ones have 6 hinges, the unmodified had 4.
You should also check this before any airtest as the elevator power off limits are slightly different.
S&L