Competitiveness and Success Caliber in Academia
No, it's not too late, my former spouse finished a doctorate when over 40 and had a great career afterwards.
But you seem to have an odd view of academia, especially when you write about "competitiveness". That seems to imply that for me to "win" you need to "lose". A zero sum game. It ain't like that, and making it like that will only harm your chances of success.
Academics normally work for personal success. They want to do good work. They strive to extend what is known in their field. But one of the best tools for that is cooperation, not competition. There is no reason for me to think that I'm better or worse than you if I'm doing what I like and produce valid results - perhaps with your help. Or you produce good results with mine.
In fact, many people rise to the "top" in academia for purely random reasons. They choose to work in a field they find interesting. But at the same time, many others, seeing the history, choose to do the same. The field becomes "hot" and so some of its practitioners are seen as hot as well. But it was just chance in many ways.
But the really big breakthroughs have often/usually been the result of teamwork. The fact that many breakthroughs in computing came out of Bell Labs was due to the close association it provided among good people. Those people reinforced one another's ideas in a synergistic way.
My advice is to do what you love. And find others to work with you to achieve success. It can be great success or not, but if life is rewarding it is worth it. You don't have to "beat" anyone.
Also, prominence is a mixed blessing/curse. You will get asked to do more than you want to do. You will give yourself an ulcer if you don't learn to relax. Your personal life may come under a microscope. If it comes naturally you will be able to handle the pressure as it develops, but if you are overly competitive you will find few allies. Relax. Focus on the science, not the success.
A few points-
28 is not too late at all. You still have a tremendous amount of time. We all mature at different rates. Some rush and graduate from undergrad by 20, then speed through a phd program by 24. Some are very successful doing this, others are not. From a personal standpoint, I took a 5-6 years between undergrad and starting a phd to work in the field. I have found that this experience greatly enriched my scholarship.
There is a lot of good work in academia. I do not believe that the majority is crappy, most is very good, and very necessary work. And the other thing you must ask yourself is "good work to who?". What is considered good work by a policy maker might be different than an academic.
Failing out of a phd program is not the end of the world, you wont be the first or the last to have this happen to them. You just pick yourself up, transfer to a different university, and graduate.
To specifically answer your question:
a. write
b. present your writing in conferences
c. publish your writing in journals
If you publish 3-4 papers a year as a first author, there stands a really good chance that in a few years you will start to make a name for yourself in your field. You do this over a decade and you will be a tenured professor who is a prominent member of your field.
Thats the reality of academia, you cannot get away from having to write and publish. Eventually you will reach a point where your time is better spent writing grants and managing a lab but you have to write/publish to get there.
How can one survive in academia beyond publications
The short answer is that it's nearly impossible to survive in academia without publishing. You want to make an impact and push forward your ideas? You have to publish them, shout them out to the world!
there are thousands of crappy researchers and only a small number who made a serious impact
This is again true, it is very hard to have a significant impact in academia. You need a combination of skill and luck.
You had a couple of setbacks, worked with people you didn't get along with, and the clock has been ticking in the meanwhile. Is it too late? No! I only finished my bachelor's degree when I was in my late 20s, and I know many others who did the same. Not finishing your PhD successfully is not great, but is not necessarily a "black mark". We are all human and stuff happens.
What you really need to succeed in academia is drive, and a willingness to learn from your failures. I would say that these are necessary, not sufficient, conditions, but still important.
Good luck!