tsschuster wrote:slowdweller, how did you go about securing funding? In the past I have not received funding for my work (besides an REU), and I imagined the funding situation might be worse if I was not even a current student. Also, did you do research with a researcher at your own institution? There's always a fair amount of chance involved with getting a research position, so I am considering emailing at nearby institutions if no positions at my university are available.
I am not too sure how to aim for getting a publication out of a position - I suppose this is something I should discuss with potential advisors.
Well my situation was a bit different. I did research at an institute in my home town, which is outside the US (whereas my undergrad was at a US place). I had been talking to my supervisor, doing informal readings with him during my summers, which I would spend at my home town. So I knew him fairly well before I started research with him. Since this place barely had a PhD program, they were able to fund external RAs in the past, including me for a very short while.
Definitely discuss publication prospects with your potential advisors. This is why I said choosing a supervisor carefully is very important. You want someone who'll assign you a project which you can approach and work on independently if needed*, and ones which can be finished in a few months time. Honestly, publishing is the only way your application would be significantly improved, as you're pretty strong in every other area, so there's no point in taking a year off for research if you aren't gonna push for publishing.
* I stress independence since you really don't want to depend on the availability of your advisor. You'll be working on such a short time frame, (a few months) that if your advisor has to leave for a couple of weeks in the middle (which will happen), you will have lost a good amount of time if you can't work independently during that time. Your progress will greatly suffer if something like that happens.