Just play a bit of devil's advocate here (actually, students' advocate.)
I feel it's unfair to say if a student just put down some relevant answers, then he/she is just trying to slide by. To lecturers all these appropriate answers are like a well organized wardrobe. We can immediately tell if the answer is spot on or is beating the surrounding bush. However, for students, their wardrobe is their whole dorm room. New information is being incorporated on a daily basis and students may not have enough time and experience in applying the information to make the organization happen before the exam date.
Just because the concept of "you should meticulously answer the questions" was demonstrated and stressed in class does not mean it can be successfully applied in exam because there are a lot more stress and a lot less sleep the night before in an exam condition.
Because the expectations are different in both entities, once you have delivered the exam back, I believe the immediate reaction from them will not be "I should pay more attention in class," but more like "this lecturer is a very unreasonable grader (or anything more profane/derogatory.)" A 35% average is not unheard of; a 35% average plus a group of eager students who want to make their final exam right is something I've definitely never heard of. They will hate you and the atmosphere in class will deteriorate.
All these are to say, if you're going to unleash this chaos, you must be 100% sure you don't bear any problem or fault. From all the related posts of yours, I couldn't help but wonder why this change (from granting partial credit to everything has to be right on or you'll get a zero?) To make sure there is at least some reliability, I'd suggest picking a few papers from the low, medium, and high tiers and give them to a couple colleagues with your new grading scheme and ask them to grade in their own privacy. Check with them and see if their scores are different and discuss why.
I also love the idea of @earthling about interviewing with some students or class representatives.
In future tests, I'd suggest instead of using the new strict marking scheme all across, use a separate system to denote questions that will be marked strictly (for instance, with a *** in front of the question or dedicate a subsection for them.) This is to allow you to phase into this new scheme slowly. The information you gain in the process will also help you refine your questions. Students will not take such a big blunt, and they will have a chance to see these questions as a challenge rather than a threat.
To conclude, I'd like to share this inspiring quote (which I unfortunately don't know to whom I should attribute):
Teach the students that you have, not the students that you want to
While I fully embrace the idea of teaching the students to be serious and meticulous, I'd still consider an overall positive learning environment takes priority. And if I have to relax my criteria somewhat, I will do that within reason. This 35% ordeal is an unfortunate event; I am really sorry that happens but can't help to also think that this is tainted with some overly zealous expectations, and I do hope you'll fine an optimal decision soon.