Loop and Merge, and randomizing sets of questions

Hi
I am trying to use Loop and Merge for a survey while also randomizing sets of questions. I am doing a survey about (imaginary) companies and gender. So I want to use Loop and Merge to pipe in information about a random company from the Loop and Merge list. Then I want to ask questions about males at that company, and females at that company. BUT, I want to randomize the order of which gender's questions are displayed first.
I can't use the in-block question randomization because it randomizes by individual question, not sets of questions. And I can't split the male and female questions into two blocks and use the Randomizer within the Flow, or else I won't be able to ensure that the company randomly selected from the Loop and Merge for one gender's questions will be the same as the other's.
I guess what I'm looking for is a way to read which random selection from the Loop and Merge has been piped into one block so I can use those same values in another block.
TIA :)