I dated a piano major in college and I tried, with very limited success, to learn how to play the piano myself. She told me, “If you’re going to make a mistake, make a loud mistake.” You don’t want to play the piano nervously and hesitantly. The same is true in research.
If you deviate from a well-established research norm, do so boldly and explicitly. Say something like “Although this quasi-experimental study has some limitations, it avoids many of the well-documented problems with a randomized trial” And then elaborate. Don’t apologize for your research design. Brag about how it is the best approach for this particular problem and explain what advantages it offers over a randomized trial.
A bold approach sounds dangerous, but actually a timid approach will hurt you here. If you use an approach that is commonly thought to be weaker, and you avoid talking about it in the hope that whoever is reviewing your work won’t notice, bad things will happen. They will hold the weaker approach against you anyway, but they will also conclude that you are naive and unable to recognize the well-known flaws of your approach.