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.