Funding is a key issue. If you can get external funding then you will be snapped up, otherwise you will enter the competitive application phases for a finite amount of money allocated to whatever PhD projects are being offered by the universities you are interested in. You should spend some time on findaphd.com to see whats out there, in particular with attached funding, but not having funding immediately shouldn't stop you applying. At my institution, supervisors are required to approve applicants on the basis of their suitability - not whether or not they come with funding already in place.
So, contacting potential supervisors early is only to be in your favour. They will be interested in finding the next student to complete the project and your being keen, showing confidence and with some gusto will stand you as a good prospect - all other academic matters considered. Contacting them now before the heavy teaching/assignment/marking loads are underway is definitely the best foot forward.
no publications to my name, with a possible but not guaranteed one coming in February, which I've heard may be an issue.
Sorry what would be an issue here? You are not even whats called an early career researcher yet, so why would it be expected that you have a publication list? I know some acheive this at Undergrad or Masters level, but publications are not a prerequisite at all. A bonus perhaps - but nothing else. In fact, I know of several PhD students who finish and go on to long post-docs and still don't produce papers until their second year of the post-doc. They do tend to produce several papers at this point though.
Final note on the cold call approach. Just be polite, express interest in any relevant works that the supervisor has been involved in i.e. "I read your paper on XYZ with interest and... it is relevant to my study because... etc.", and make sure you highlight your strengths, skills and experiences that are relevant to the position. Assuming this will be via email, dont forget to include an email signature showing your contact details and ideally send from your academic email account of your current institution.
All considered then, just go for it. There is nothing to lose and everything to gain.
Best of luck.