I'm not in a similar situation, but I did my bachelors in applied/computational math and got into some PhD programs for applied math this cycle, so I can at least give you a run down on the applied vs. pure math angle. You say that

The reason being that I've always wanted to pursue my interest in the field of mathematics

But this is kind of a vague statement. What particular aspects of math do you enjoy? You say you've taken "engineering mathematics" but nothing else, so do you know for sure you want to go the applied route vs. pure? One thing that could help you now is to enroll at a local university. In particular, on the pure math side, you can sample real analysis, algebra, and topology. This is good not only for pinpointing what your interests are, but also to get those courses on your transcript. You're also going to want your statement of purpose to be focused and meaningful (even for

I think a good mGRE score can help your application stand out given that you won't be coming from mathematics background, but I'm not sure it's really a substitute for taking the actual classes. You will be competing for admissions against students who have both done well on the mGRE and taken the requisite courses, and at the end of the day, the GRE is just one component of your application. For schools that require it, a poor score can tank your application, but a good score is no guarantee of success. Also keep in mind that many applied math programs don't require the mGRE score; it's to your advantage to submit it if your score is good though.

Now, some schools include applied math within their pure math department (UCLA, Berkeley, etc.), meaning that you would be taking courses tailored to a pure math degree. Other schools have a separate department entirely for applied math (U Washington, Maryland AMSC, Rice, Stony Brook, etc), and the courses are much more varied. Keep in mind that there aren't many dedicated applied math departments, and their curriculums can vary significantly, though the core courses (calc 1-3, ODEs, linear algebra, analysis) are similar. For example, my undergrad curriculum was something like:

-Calc 1, 2, 3 & ODEs

-Real analysis

-Linear algebra

-Numerical methods for PDEs

-Optimization/Linear programming, integer programming, graph theory

-Numerical analysis, numerical linear algebra

That would be the bare minimum for the degree, and is more of a broad survey than anything else. It was up to the individual students to flesh out their studies to suit their interests. If you're looking to take bridging coursework before applying, this could give you some idea of what to look for. You ask

How do I explain my lack of courses taken? Is there anything I can do to satisfy these missing credits?

I don't think there is anything to explain, other than the obvious fact that you chose to major in computer science in undergrad. You can mitigate that by taking some higher level math courses and showing the admissions committees that you're committed. Also, there is most definitely some overlap between computer science and applied math. If you're interested in a specific subfield of applied math where your CS background will be an advantage, definitely highlight that. Hope this helps!