phd - Boost grad apps profile without getting a second master's: Subject GRE? Self-study? Soft skills?

In general, how does one boost PhD admission profile?

In my context, same question but besides getting a master's in pure math. (See here and here)

Here's what I got so far:

1. Employment not specifically in research for soft skills boost (I have specific career goals in case I am not good enough for academia)


2. Employment specifically in academic research (I've seen job posts that look for research assistants) for research experience here I think?


3. Employment as a research analyst in finance


4. Tests e.g. GRE Subject


5. Self-study

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What else?

1. 
   

   work for a professor for a research project like here I think?

   
   


2. 
   

   Or pay a professor to supervise my own research projects like here I think?

   
   

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My context:

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What about the GRE Subject?

• I was suggested by one of my professors to study for GRE Subject, but I think that was in the context of his applying to master's having had only a bachelor's.

On one hand:

• The GRE Subject may make up for low grades or the fact that I haven't had complex analysis, number theory, graph theory and abstract algebra. Is that right?

On the other hand:

• 
  

  The GRE Subject doesn't seem to show ability for research. Am I wrong?

  
  


• 
  

  It just seems to be able to show that you know complex analysis, abstract algebra and other things that, while are expected of math PhD applicants, are hopefully expected to be able to be learned by math/applied math master's holders, that you take exams well, know precalculus or calculus tricks or pathologicals (cf. pathologicals in real analysis are important!) and haven't forgotten very basic facts that you haven't encountered in higher math.

  
  


• 
  

  Even if I were to study the basics of complex analysis, abstract algebra, number theory and graph theory I'm not sure that that translates to a much higher GRE score. Does it? Or can it help graduate applications in some other way?

  
  



• 
  

  I mean come on, if it's just for the GRE Subject Test, of course I'm just gonna use Schaum's Outlines or a GRE Subject book instead of actually learning from a textbook. I would rather learn from a textbook, but I don't see how the learning beyond the basics is helpful for graduate applications (cf. graduate school).

  
  

P.S. Sucks if I don't stand a better chance for boosting admissions through self-study. Sigh. Can't believe there's a dichotomy between doing what is helpful for graduate school and what is helpful for graduate applications, but then again professors aren't the only stakeholders.