Is there any meta advice which mathy people here would give about how to increase efficiency in solving problems? Anything you've learned over time? E.g. I think I spend too little time thinking broadly and too much following the first approach I've found. Stuff like that.

My thoughts:

It is important to reflect after either solving a difficult problem or looking at the solution. Figure out the motivation for the solution, and try to find a framework to view the problem from that makes the solution obvious or natural. When you do lots of problems, you can begin to see when similar frameworks can cause solutions to fall out of problems that might look very different at first.

Also, just do lots of problems.

Most of my experience comes from math olympiad, here are some links from people on solving math olympiad problems (in a broad sense):

https://hcmop.wordpress.com/2012/03/23/how-to-approach-an-olympiad-problem-by-ho-jun-wei/https://usamo.wordpress.com/ (couldn't find a specific post that really addressed what you are talking about (although it probably exists) but maybe you will find some things interesting.