OK, so you've got it tough. Welcome to life, we've all lived our version of a country western song.
Now, I will offer that you may be entirely correct that trying to access your distant repeater would just be an exercise of futility. The path is just too long, signals too weak or nonexistant and no amount of antenna gain or height will get you from A to B. Consider though you don't know this for a fact. So why not try? This isn't a critical ops mission or your livelihood, it's a hobby. Everything you do in ham radio will cost you time and money and net you zero return. But you can gain knowledge, skills, experience and friendships *even if everything you do is wrong*. So why do you care if you try and fail? Or conversely, if you care that everything must turn out perfectly then you're in the wrong hobby.
In an ideal world you'd fly a drone with a unity gain antenna and map out a 3D space of RF densities around your area so you'd know exactly how high and how much gain would be required to achieve the minimum path margin you require. OK, so since that's not happening go with what you have, or what you can source. A yagi would be a good start. I have personally participated in one of WA5VJB's antenna forums and I'm here to tell you this is not brain surgery. With literally $5 worth of stuff from Home Depot a dozen people walk in to the yagi forum and out with a working antenna in less than an hour. If you're resourceful you could reduce the material cost to zero and I know you have an hour to spare because you burned that much time already kvetching here on eHam. This is a journey, not a destination. Make a plan to build the antenna then come up with different ways to test the path. Doesn't matter if it happens over the course of days, weeks or months. EVEN IF it comes up bust, you've learned about and will have a working antenna to use for other things, you've learned what you can access and from what directions, and you're active in learning and discovering in general. You may meet others in the process that can help you achieve your objective, or you may discover some other interesting thing to pursue in the process. So make a plan, make something happen. Failure is an option and is often a useful learning path.
Mark K5LXP
Albuquerque, NM