I hate to say it but I think it might also have to with the fact we are in Canada (I'm near Toronto). I do not know exactly how it is for chemical engineers, but I am a food chemist, and I had a difficult time finding a position after completing my MSc also with very little industry experience. It took over two months, and I got very depressed/discouraged by this, but finally got in with a company that did R&D/Science. I realized from talking to employers that most of the R&D in food industry had moved out of Canada back to the U.S. centralized R&D centers after the Free Trade Agreement. Additionally, I found that the food industry in the U.S. was paying their scientists much more than here in Canada, which has made me think about making the move to the U.S. somewhere down the road.
So my question is -- Are you able to move to the U.S? This may help your job prospects substantially. Also, Alberta due to the economic gains from extracting oil from the oil sands has led to many jobs for petrochemical engineers, although if the low gas prices continue, even Alberta will be making severe employment cuts.
Also, it may be worth looking at finding a recruiter/headhunter in your industry. Typically, they will bill the company from finding the right person so it will not cost anything to you to contact them (although it may indirectly as it may affect your starting salary). At very least, they will be able to objectively look at your resume and tell you honestly what is hurting you from finding employment and ways to improve your resume/cover letter, since they will have much experience with this.