In the absence of strong references, on which things should I focus so that I can gain access to a PhD program? The idea of working toward a PhD came to me very late in my Master's program. As such, my primary professors and adviser didn't necessarily coach me into PhD preparation and may have even seen me as somewhat of a black sheep in the academic community. I don't doubt that they would believe in my ability to research, but rather that it'd be somewhat of a surprise that this was an area of interest for me. 

Having said all of that, while I believe that they could give me a good reference, I don't believe it would be the "great" reference that would be characteristic of this internationally-recognized expert in their field. With this in mind, are there things that I can do to make myself a more appealing candidate to a PhD program?
PhD programs are looking for strong evidence of research potential.  We'll look for that evidence in your recommendation letters (preferably from people who know the field and know what potential stars look like), in your research statement, and in your academic record.

Get the best references you can.  You write "I don't doubt that they would believe in my ability to research", which is excellent.  They may also write about their surprise in your late interest, which will raise some eyebrows, but it's the truth, so you're stuck with it.

In your research statement, be sure to explain why you're interested in a PhD, and in particular, what changed in the late stages of your MS program to spark your interest.  You need to actively pre-empt the perception that you just want to stay in school because you want to learn More Cool Stuff, or that you tried Real Work and you didn't like it.

You also need to include credible technical detail about your research experience and your specific research interests.  (Yes, that means you need to have research experience and specific research interests.)  Otherwise, readers will wonder if you know what research actually is.  That naïveté might be excusable for someone with only a BS, but for an applicant with an master's degree, it's a serious red flag.

Good luck!