Further Randomization within Semi-Randomization

Hello everyone!
We have a survey with semi-randomized block orders, and we need help figuring out how to add further randomized conditions within the blocks. 
To begin to explain our semi-randomized design, we have six blocks that are displayed, however it is set up so that certain paired blocks are not displayed next to each other. To clarify, within these six blocks there are three pairs of two blocks making the six blocks labelled as follows: A1, A2, B1, B2, C1, C2. Our current randomization setup ensures that any of these blocks can come first, but blocks with the same letters cannot be next to each other in any trial (ex. B1 will never come immediately before or after B2).
Our issue lies in the next step of the randomization process, as we wish to follow each block with one of another set of similar paired blocks (e1, e2, f1, f2, g1, g2), however this time we want to ensure that the same letter blocks of the first set each contain the same letter blocks of the second. For instance, one hypothetical order could be as follows: A1->f1, C2->e2, B1->g2, C1->e1, A2->f2 B2->g1.
As is clear, the order of the presentation of the second group of blocks is randomized, but each letter (e, f, or g) corresponds to the same letter of the first group of blocks (A, B, or C).
Any suggestions about how we should go about tackling this problem? We have already figured how to create semi-randomized blocks , it is simply a matter of pairing the e-g's.
Thank you so much in advance!