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I killed the Psykers. Although my losses weren't as high as the author's, I still managed to win. To achieve victory, I had to do the following: I dismissed the Wyverns and replaced them with a single Troglodyte (in theory, it doesn't matter which unit you use as bait, I decided to focus on morale; in theory, I could have won with the Wyverns as well), which lured the Psykers in the first round. In the first turn, the Manticores attacked with morale (under the shield), and then the main thing is not to get hit by double attacks, and it's all simple. In the end, I had 3 Cats, 5 Eyes, and 8 Medusas left. The Medusas also got morale towards the end, but it didn't matter anymore. I could have saved the Angel by simply flying it to the edge of the screen :D
P.S.: Well, this is complete noob play, of course. Please teach me how to lose only 4 Troglodytes? Here's a reasonable question: how is it even possible to lose only 4 Troglodytes? If even 1 Psyker attacks the Troglodytes, it will kill more than 4 - that's a fact, and you can't separate the single units either... So, it's clear that something is fishy :D
P.P.S.: Save files before and after.