I would have set a simple trap for him. With a question and a followup.
Question: “Let me ask you a question that has nothing to do with any on-going investigation so that you can’t use you “FBI won’t let me talk” excuse. Mr. Strzok, you say that your use of FBI communications to express your political opinions is allowed, but no one in the FBI but you thinks this is acceptable, do they? Because they are professionals and no professional would offer political opinions about cases that they were working on to others, would they? You cannot name a single person in the whole FBI, other than you paramour, who did something similar, sharing opinions with you, thinking that it was acceptable to do so, can you? Not in the whole long history of your FBI experience.”
The question is intentionally taunting. Strzok can only either admit there is no one else doing this, thereby admitting his unique flaw and unique lack of professionalism, which, given his character, would be difficult.
However, if he suggests that it does happen with some sort of weasel wording, the response is another question.
Followup Question: “If you were telling the truth and such activities are done and seen as acceptable, you would tell us who and about who and what topics and cases they offered opinions on, wouldn’t you? You won’t do that, will you, because you know such activities are not acceptable and, if done, must remain hidden.”