As a new Ph.D. student (mathematical statistics) how should I read papers for research?
My PhD was in statistics, and I have also supervised PhD students in this field, so hopefully I can offer some useful advice.  Here are some thoughts:


Talk to your supervisor: There is no room for intellectual shyness in that relationship.  Your supervisor is not going to be upset with you for asking questions, evening if it is something you think you should know how to do already.  The fact that you even think to think about this is a good sign, and your process is quite impressive.  Don't be shy.
Streamline your process: Your process sounds quite comprehensive already.  Personally, I find that writing a short summary in your own words/notation is probably the most useful exercise to understand math papers.  Some of the other stuff you're doing might be a bit excessive, especially if you're only getting through one paper a day.
Learn the maths, expand your tool-kit: In a mathematical field, in additional to understanding the specifics of the paper you're reading, you also want to use this as an opportunity to gradually expand your mathematical tool-kit.  To do this, make sure you understand the derivation/proof of each result, and if you see an unfamiliar mathematical technique, talk to your supervisor about why it works, and when you might deploy it.
Learn to "see the matrix": Think about the intuition of each method and and make sure you can describe it intuitively.  When reading mathematical theorems, ask yourself lots of questions:  Do I understand this result and its relevance to the field?  How would this be applied in practice?  Do I understand the proof(s)?  Are there other ways to prove this?  If there are necessary conditions for a result, do I understand why they're necessary (i.e., why does the result fail without them)?  If there are sufficient conditions for a result, do I understand why these are sufficient (i.e., why does the result hold in this case)?
Jot down your own ideas: As you read the literature, jot down your own ideas for possible extensions and interesting questions that come out of this.  At first these might be quite ill-posed, but you can gradually refine them as you learn more.