I'm considering two carbon sequester strategies that should be cheaper than digging a hole in thick clay.
1) Using pingos by hollowing them out with hot water or steam and replacing with wood/chips and peat pore water. The disadvantage is this might dry out upon thawing or drainage as AGW happens.
2) Hydraulic fracturing of a formation at or just above the locally lowest elevation bedrock layer in an area. The fracture substrate would be pore water, wood chips, and some sort of clay slurry that should prevent drying out of the "matrix" even if bordering an aerated vadose zone layer. This strategy would scale but might be as or more expensive than digging clay; injecting clay might be no better than digging in it.