Interesting idea.
The first thing you should concentrate on is to optimize your plan on power usage. 15-25W for relaying some data (<100Mbps I guess?) for a few dozen meters sounds at least an order of magnitude (if not two) high to me. Remember your links are directional.
Even on a bog-standard WiFi link we are talking about 1W, and that would have a longer communication range than what you need, and it would be omni-directional (spherical), and WiFi is notorious for poor power efficiency. LTE is able to communicate with cell tower kilometers away at well below 1W. You need power-optimized communication to need less energy harvesting.
I guess you would replicate hundreds if not thousands of these repeaters; it would mean that they are not one-offs, and you could concentrate in optimizing them. While 15-25W is AFAIK impossible to safely harness from the wires, if you can drop the link consumption to, say, 1W or less, then a small solar cell with a li-ion cell becomes a real alternative, even if you failed harvesting energy from the power line itself.
The delay caused by the number of repeaters would become an issue (latency is really important in modern Internet usage), unless you can come up with some really clever low-level protocol stack to do the job. I guess you should still minimize the number of repeaters as well, most of the time the power poles are in a nice straight line so if you have a LOS between ten poles, you also have a LOS from pole 1 to pole 10, directly. Then you'd use higher density of repeaters only when the power line changes directions.
In any case, I guess this will be a demanding project, requiring a lot of RF and network protocol expertise.
Finally, if you can afford to install devices to each or most power poles, don't you think you couldn't just as well install some optical fiber there, hanging well below the power lines, but still out of reach? Wouldn't that do the trick much more easily?