If the furniture came off an 'old model' 20 gauge 870 (which was made on a 12 ga. sized frame, last letter in the serial number is X) then the frame sizes are the same. If from a newer model 20 (receiver code K or U) then the 20 ga. frame is smaller.
Used wood both walnut and beech/birch abounds for 12 ga. 870s, there are multiple sets for sale on eBay and similar sites. It's relatively easy to shorten stocks and attach new recoil pads as needed, no reason to put up with a stock that doesn't fit or a pad that's too hard to help with recoil.
lpl/nc