You'll need to acquaint yourself with voltage drop calculations / a voltage drop calculator. Basically, the longer the cable the higher the resistance. This resistance reduces the voltage at the end of the cable and causes the cable to actually heat up a bit. To counter act this, longer cables need to be larger wire gauge (lower number). The requirements in the national electric code for burying a 240V run are significantly more challenging than say a GFCI protected 120V UF line. Lightning would be another fun challenge (though I don't think of AK as the lightning capitol of the US) with the web of wiring you describe. Bottom line is the way you envision this working is likely to be pretty difficult to do safely and effectively, not to mention expensive. I think you're underestimating these challenges. There are ePoE cameras that can go a bit longer than the standard 328' but it would still be challenging. The notion of totally hiding the cameras and all of the equipment inside hollowed out trees also isn't the most realistic. Try not to take offense at this, but this kind of feels like something I would have dreamed up when I was 10 years old.
A much more practical option would be a few clusters of cameras on a tree or pole with a wireless link back to the house and likely powered directly by a small scale solar system (math required). An off the self option to consider would be Cuddeback CuddeLink or other game cameras which send images wirelessly.
There are also long range motion sensors that could have some potential (these can get expensive too). On the most expensive fanciest end, there are radar based systems that can generate a bearing and distance to target and direct a PTZ accordingly (stoopid expensive, but so it your imagined project) also in the category are OTDR fiber optic intrusion systems (you'll find research papers on the subject, but good luck buying one).
I would start with a few cameras on the cabin, maybe a PTZ get a feel for how they work, what they can and can't do and adjust your plans.
