If the boards are plastic, then your best bet is to simply replace them. If you try to sand or re-surface plastic, it will simply get so fuzzed up as to be worthless..
For wood boards, look for a woodworker's shop, preferably one that makes custom furniture from raw wood. The tool that you need them to have is a benchtop planer. It's pretty simple for them to use, in 4 easy steps.
1. They adjust the height of the planer for somewhere about 1/8th inch or less than the existing thickness of your board.
2. They run your board through the planer. That smoothly cuts off a level amount of wood across that surface of your board. That side of the board will be pristine and smooth.
3. They drop the height of the planer knives about 1/8th inch or less.
4. They flip your board over and run your board through the planer, so that the other surface gets re-surfaced.
Total time: maybe 10 to 15 minutes. Probably less. Mostly, it depends on how much time it takes to write up the order and process your credit card. In terms of real work done, mostly, it's a matter of careful measurement and setting the thickness properly. Running the board through the planer takes less than 1 minute.
Then, it's up to you to re-oil your newly resurfaced board.