I had a lot of turbine experience prior to taking a job flying multi engine piston airplanes. One of my co workers, aware of my past, asked if my former employer would hire him so that he could log 100 hours of turbine time in order to apply at a specific fractional. Yeah, sure, what a great deal for my former employer. Lets get you trained so you can log that 100 hours that will make you so much more skilled and experienced so that you can leave after 2 months. And people wonder why there are training contracts. Unfortunately, this attitude seems more and more common with newer pilots. The whole idea for minimum experience is to progress while you're building time so that when you reach or, ideally, exceed minimums, you're a sharp, trainable, employable pilot. Flight instructing is great and I highly recommend it, but I've tried to train flight instructors as new hires and a few were terrible. You could tell they didn't progress while building time. Instead they shortchanged themselves and probably their poor students.
Your plan to log 12 more hours seems to me to be similar. My question is how did you get your first 13? If you bought it, why not buy more and be done with it. It will all pay off in the end, right? If you find someone with a twin to ride around in, are you going to be able to explain in detail that aircraft that you have logged 13 hours in to the HR panel? Probably not, and if that's the case, its almost the same thing as pencil whipping it.
P.S. 3000 hours in the right seat of a caravan has to be some kind of record.