This picture looks really very good, but the problem is that you painted Livyatan more or less exactly like a modern day sperm whale with a different dentition and the eye at another position. But this animal was very different, and it was most probably not that similar to Physeter at all. The line of Livyatan and modern sperm whales divided already a very long time ago, even before the lines of modern sperm whales and pygmy sperm whales divived. So we can be quite sure, that anatomical traits only seen in Physeter but not in Kogia, were also not present in Livyatan. For example the shape and position of the dorsal fin, which is still normal in Kogia, but modified into a series of humps in Physeter. The position of the nostril is also only in Physeter at the very top of the spermaceti organ. Kogia has a totally normally positioned blowhole above the eyes. The wrinkles seen in modern sperm whales seems also some sort of novel feature. The shape of the mouth was also probably somewhat different in Livyatan, as there was probably more soft tissue of cheeks and probably also lips covering the upper teeth at least in the more posterior part of the jaws.
To undertstand the relations of Livyatan with other whales, it´s good to take a look at this phylogenetic tree: de.wikipedia.org/wiki/Livyatan… Modern sperm whales are among the most specialized of all whales, and they have a lot of weird anatomical traits, like giant size, (usually) non-erupting upper teeth, a giant spermaceti organ which covers the whole rostrum, multiple "humps", wrinkled skin (it´s not always wrinkled BTW), a fully anterior and lateral blowhole and several other things. But in the past, there were much more kinds of sperm whales, which were similar in some anatomical traits to modern sperm whales, but still very different in others. For example, the ancestral sperm whales were not giants, but ranged from the size of a big dolphin to a big orca. They had still upper teeth, and their skulls show that in some very early lines, the spermaceti organ was still not covering the whole snout (like in Zygophyseter for example). Some of those very early sperm whales were probably just fish-eaters with comparably thin rounded teeth, but several lines evolved a more predatory way of live with massive interlocking teeth with sharp shearing edges, for example Brygmophyseter, Zygophyseter and Hoplocetus ritzi, which were probably very similar in ecology to modern orcas (which have also a very wide range of different prey animals), other were quite small but had massive jaws and teeth like Acrophyseter. The line which did lead to Livyatan was also different. It was still closer to modern sperm whales than the forementioned species, but still not as close to modern sperm whales as pygmy sperm whales are to Physeter catodon. After all, Livyatan was totally unique, and in its anatomical traits to some degree just parallel evolutions to both killer whales and modern sperm whales, but based on the bauplan of archaic sperm whales. It´s all somewhat complex and not that easy to explain. The problem with the life-reconstruction in the museum it that it includes some errors too.