Have you considered flash? A cobra-head zooming flash going to 200mm tends to have a guide number of about 70 at that length. Its reach at F2.8 and ISO25600 would be 400m. For full exposure.

When working with a 200mm lens, 400m is actually quite a distance. Though you would want to work with a dark background and a lit subject, so you'll likely reduce exposure time to your flash duration (typically 1/200s) and possibly dial down ISO a bit.

Birds of prey can sit still a lot better than photographers so you could use longer exposure times, too, but particularly with the longer lenses that would require use of a tripod.

As you can see, with 1/50s and the fastest lens, your best is a washed-out silhouette against a noisy backdrop.

There are of course a number of disadvantages for a flash shot, too: probably the worst is that with a shy subject at a good distance you get to have exactly one shot per opportunity. Another is that structures such as pylons might be equipped with reflectors or reflective signs that basically halve the distance to the camera. While you can edit them out in post, they will mess with any metering (like TTL).

Also autofocus is not going to do an overly convincing job.

And there will be the red-eye equivalent of birds' eyes, and particularly eyes with good nocturnal vision will be affected.