How can I overcome academic "researcher's block"?
Forgive me but I'm going to just wildly speculate here and hope that you find a bit of value in it. Perhaps you are just the sort of thinker that thrives on the synergy of working with others and getting ideas bounced around and reinforced (or shot down). That doesn't make you less of a mathematician, of course, but just represents one way of getting all of the pieces together. 

It seems like you thought of yourself up to now as the 'junior' member of your circle and now the others have died or retired and so you are left 'alone'. In fact, IMO, you are left, now, as the senior member, but you don't need to continue to be the 'only' member. 

Try to build up the circle again with new junior members with whom you can interact, building up their ideas as well as your own. It will give you that synergy again, if this is indeed the issue (like I said, speculative). A local circle is best, of course, but today's communication resources give additional options if learn to use them intensively. 

And you have the opportunity to become the master that those younger scholars look up to and revere as they grow into the profession. Very cool. 



One additional factor might be at play. When a person tries too hard for too long at intellectual activity, the brain sometimes rebels and shuts down. A break is called for, especially a break that gets the blood flowing, such as physical exercise. Physical exercise that also engages the brain but in a different way from the normal research mode can be helpful. I use Tai Chi for this as it is a mind-body fusion exercise, though not aerobic. When younger, I used cycling and x-c-skiing and such though they didn't have the same mental component. But an hour or so break for physical exercise can sometimes invigorate you. 

And since the mind works subconsciously as well as when forced, sometimes insights magically appear during or immediately after a break. Even a sleep break.