Thoughts on if it's possible to succeed in math @ PhD level w/o natural ability in quant reasoning? As someone who has a relative deficit in quantitive reasoning (63%ile) vs. verbal (97%ile), but a strong interest in applied math, is it possible to be successful and competitive at the PhD level?

I am committed to putting in the effort, and I want to believe that this is possible - but it is very daunting.

EDIT1:

To flesh out the q: 
I’ve taken Calc 1, Calc 2, Calc 3, Stat/ w Calc &amp; Discrete Math. I got a B+ in the first 2, A in the third and 4th, and B in the 4th. Taking Linear Algebra/Real Analysis and expecting an A or a B. Calc 1&amp;2 and Discrete math were taught at the liberal arts college I went to where I received a BA in the humanities. After my BA in the humanities I pursued ad-hoc post-bac in math so that I’d be able to apply to grad school. Calc III and Stats with Calc were taken at Columbia and LA/RA At Harvard. 

I will say, I have improved dramatically since I first began taking math (w/ Calc I &amp; II).

The test I took was WAIS-III full scale IQ test, designed to be taken with no preparation and administered at a world renown  neuropsych facility. 

Regarding the GRE, I expect I’d be able to score in a percentile on par with other prospective applicants.

My plan is to apply to a terminal masters, ace that, and the go one to apply to PhD programs.

Lastly, I have significant adhd for which I was unmedicated in undergrad and may but may not account for relative split in grades before and after.

EDIT2:

I'm specifically interested in applied math. I want to pursue it because I find it challenging and interesting and immensely rewarding when I grasp a concept -- and I want to go into a field that helps people.
To know whether you can do an applied math PhD, the question to ask is: did you succeed in difficult math, science, and computer science courses in undergrad, and do you have professors in relevant fields willing to write you a strong recommendation? General aptitude tests are dramatically less informative. This is not to say that, if you’re correct that you have average quantitative reasoning ability, a math PhD might not be the wrong choice for you. It’s just that you have other, much more refined and relevant, information available to judge by.

EDIT: Based on your edits, I’d say an A in Calc III at Columbia is more informative than the IQ test. That said, you have few advanced courses-only one, once you finish real analysis. So there’s not much evidence yet of your prospects. You’re in a plausible position to apply to master’s programs, and if you get into a good one, you’ll a get a much clearer idea of yourself there.