Surely this calls for data analysis? I’ve seen Economics papers on publication and placement for PhD students by programme, and I think for Sociology. There are almost certainly relevant publications for your field and if there aren’t you could probably get a publishable paper out of writing up your own research.
If you’re in Year 2 of your programs and on track to have three publications by Year 5 your personal probability of getting a tenure track position must be 50% or higher, not 25%. Again, this calls for data. The 25% of your programme’s graduates do get placed; what kind of publication records did they have on graduation? Compare yourself to the reference class you want to be in. I am almost certain PhD graduates in PS’s top programme have on average less publications than you do already. Most Harvard/MIT Economics PhD graduates never publish a paper. I don’t know what Political Science is like but if it’s similar your publication record is going to look pretty good.
If you’re considering industry why not look for the skills they like and try to publish something that would use those skills? Look up Economist jobs at Amazon, or read Susan Athey’s advice for people who want those jobs.
Can’t you staple three papers together with filler/linking material and call it “Essays in Political Science” or a narrower topic if you’ve been focused?
I suggest emailing Chris Blattman and Bryan Caplan and asking for advice. Greet, be brief and to the point. I suggest Blattman because he works as a political scientist though he was trained as an economist. If your statistical skills are good you can do very well outside academia. Amazon Economists (PhD required) are getting over $175K starting. Bryan Caplan I suggest because he suggests academia is a truly amazing job for some and the competition isn’t that high.
https://www.econlib.org/jason-brennansgood-work-if-you-can-keep-it/