No Mystery. The number 56 7209 has been misread or your typo. Its actually 56 7029. It is not a part number, it's a BSA PATENT Number and appears on all barrels. So same number on A7, A10, (Standard and Thick Flange) variants, plus early narrow and later wide fin types. It's the number on the back of the tappet housing. First seen on the A7 Longstroke.
Barrel part number is cast on the front face of the mounting flange. 67-1210 is correct for a thick flange wide fin barrel. Look for a bore of less than plus 60, giving scope at least for one other simple rebore, then consider broken fins, cracks, pulled threads. These frequent faults detract big time from it's value but are fixable, while adding substantially to the cost if requiring professional repair.
Swarfy.