I wonder if actually making the rows early-redeemable, for less than the proportionate total reward, could also help.
For example, in a 4x3 card, maybe each row of 3 gets you 15% off if redeemed early. In this way, you're always close to something with provable value; you're more likely to value/carry/protect the partially-completed card; but you're also still likely to go for the 12-for-100%-off rather than stopping at 3-for-15% / 6-for-30% / 9-for-45% off.
(The various App punchcards bring the possibility of running many more incremental tests in this area, and novelties like 'awakening' dormant customers with a gifted stamp or two.)
Grouping focuses people on immediate completion (visually completing a line or block) and keeping the relevant numbers small (3 and 4 instead of 12), even if the groups have no nominal significance.