Relearning how to work (becoming much more efficient). Is it even possible?
It is not possible to give you a satisfying answer. The best I can offer is two anecdotes a friend of mine told me today (and they are first hand and 100% legit).

First, he goes to the supervisor, for the second time, with a bunch of paper, asking whether he should study them. The supervisor takes the papers, throws them to the ground and walks over them. Then says: "Studying is useless."

Second, the supervisors asks him to do a computation by the next day. Friend comes back and shows the calculation. The advisor writes a line of code on the computer and presses enter. The computer shows the same answer of the computation which took several hours.

Bottom line: there is ample room for improvement in terms of speed. Achieving it might require, surprisingly, to understand less and to study less and to give up on many preconceived notions about the subject and about how research work as well as about how yourself.

If you feel like the subject is important and close to your heart, give it a try. Many people start a PhD in their 30ies. But don't be silly, do:


Ask for advice before making choices.
Think carefully when picking your advisor.  
Lay out many plans B and be ready to execute them.