Is it possible to do a two-step randomization?

You can achieve this (at least currently) as follows:
At the TOP of your survey flow, above any of the question blocks, put in a randomizer.
Within the randomizer, put in 12 Embedded Data steps eg:

• Group1 = SET


• Group2=SET (and so on, for the 12 groups you currently have)

Tell the randomizer you want it to select 3 of those 12 steps evenly.
Now go back to the survey, and in each of the current blocks, apply logic to EACH QUESTION (not the block itself) so that the questions in what is currently block 1 all have logic that says it should be displayed if Group1 = SET (same with the questions in block 2, where Group2 = SET)
When ALL of the 48 questions have logic set on them that corresponds with their current block groups -- move the questions into a single block, and put randomization on the block. Qualtrics will probably throw a warning about display logic and randomization, but this appears to work, and allows for a randomized selection of the "groups" while allowing all 12 of the net questions to be presented on a single page in random order.