A lot of caliber recommendations out there are significant overkill, based on limited data. In cases where we do have data, calibers signicantly less powerful than recommendations often prove surprisingly effective.
For example, in a survey of 104 grizzly and polar bear attacks with handgun calibers, there were only 3 failures, all of which involved firing after the bear had already caused damage (an automatic failure) or completely missing[1]. You'll often see guys carrying 44 magnums in grizzly country, but the evidence seems to suggest that common 9mm rounds are effective enough. Even the lowly 22 rimfire is represented in the data with success against black bears (but not polar bears). I don't know anyone who would recommend 22 rimfire for deer let alone bears.
Given this, I think it's reasonable to select the venerable 7.62x39. This is a common chambering for semi-automatic and even automatic rifles with high-capacity magazines, which would obviate the need to load each bullet individually. It also is easy to obtain armor-piercing rounds in this caliber if penetration is your concern. This is still a punishing round to fire a lot of, but with a modern recoil management system it's manageable.
Additionally, the heart is a small target as well, but luckily most hunters' experience is that larger target including the lung and liver can provide reasonably ethical kills (i.e. the animal dies quickly without a prolonged tracking during which the animal suffers). For most animals striking the scapula proves disabling, allowing for an easier follow-up. So just aiming slightly forward of center of mass should be sufficient--no detailed knowledge of anatomy or high-speed, high-precision shooting needed.
All this is to say that with a different approach, killing what can only be described as a stampede of 30-50 hippos in 3-5 minutes isn't as implausible as a more conservative approach might make it seem.
[1] https://www.ammoland.com/2021/06/handgun-or-pistol-against-b...