How to rectify no publication after PhD graduation? My situation is very strange.

I have completed a sociology PhD from a well-regarded university. As I was a part-time candidate and holding a full-time job in the private sector, I guess my supervisor did not impress on me the importance of publishing. In addition, the university has no requirements to publish in order to graduate (though all academics there, including my supervisor, have strong publication records).  

I cannot blame my supervisor entirely because I should have known better (but doing it part-time outside the university environment and in a role that puts no importance to academic research are the main reasons for my current situation). 

I am now realising that lack of publication is severely restricting my career aspirations. For instance, I want to pursue university teaching (one of the main reasons for me to do my PhD) but I have not had any luck so far because most roles require "a proven / demonstrated record of publication" etc. Another example is that I want to establish a credible standing for myself and a list of publications would certainly help in this regard

I can point to various "research" I have done in my current role but they don't count as research in an academic (peer-reviewed) or formal sense.

As I have graduated now, I am no longer affiliated with any university. To make matters worse, my supervisor is mostly out of country doing research etc., so he is largely uncontactable. I can use my company's name, but it is a small obscure firm in the overall scheme of things. My PhD is in the field that I am currently working in, so I can get some credibility in that sense.

I have thought about open access publishing (in reputable journals) and turning my PhD into a book but unsure about them.

QUESTION: How do I rectify my situation of no publication?
Summarising details from the comments, the final verdict would be 


  Start publishing now!


If you did qualify as a PhD in a reputable university, you should have the ability to publish a peer-reviewed paper. And so it seems that there is no excuse out of this way. As stated by @GEdgar, academic affiliation is not a primary requirement for paper publication. The only way to rectify would be to start framing your manuscripts today.