First I would like to apologize if this post breaks any rule regarding career advice or opinion-based questions. Given that construct QFT (CQFT) is a rather small community, I found this is the only site where some current/past practitioners can chime in.

For an idea of my mathematical level, in terms of analysis I have finished Folland's book on real analysis (which is mainly about measure/integration theory and basic parts of functional analysis) and I am currently going through Reed & Simon's book on functional analysis. I am also comfortable with general topology and I have gone through most of Tu's book on (smooth) manifolds. I also know a little bit of PDE theory. On the physics side of things, I am largely self taught and I have gone through most of Folland's book on QFT, Hall's book on quantum mechanics, and a small smattering of Peskin & Schroeder. The major physics topic I am not very familiar with is E&M, which makes learning from physics books difficult as they often teach QFT through QED.

I am interesting in going into CQFT, but I am a little puzzled on the best way to go about it. I read a few other questions on here that provide some very nice resources. The problem I am having is some of the math-oriented books assume too much math and the physicists assume too much physics (and speak in a completely different language than what I am used to as a mathematics student). Should I be learning QFT from only CQFT texts, or should I use traditional/heuristic physics books as well to get an intuition about the subject? Is there any other approach that is recommended?