I've never hunted DG and probably never will. There are a number of reasons for that but typically these fall into one of two categories, financial and ethical. I simply mention this because others have commented on there own personal experience of which I have none.

If I were to engage in DG hunting I'd want to carry either a double or a Mauser. When I say Mauser I mean an action incorporating all the safety features found in the 98, rather than something necessarily built by the Company. So a Brno, for example, in an appropriate caliber would do just fine - assuming it functioned correctly of course.

If it were a double it would have to be what I would describe as a 'proper double' and by that I means two separate ejectors, separate locks etc. Essentially two complete rifles joined together and sharing a common stock.

So basically I'd want a firearm that, should the shit hit the fan, gave me as much of a safety buffer as possible without detracting from the classical nature of the hunt.

One the subject of supposed Mauser system failings, yes, the split lug probably isn't as good as a solid one but as far as I'm aware this is mostly theoretical. The gas issue again is, as far as I know, theoretical. Although some other actions may handle gas better (?), the Mauser 98 does it better than most and certainly as well or better than any of its contemporaries.

The Rem 700 may well, as you say, cycle successfully in an inverted state BUT, is that actually a relevant consideration? A Mauser may well function perfectly while submerged in heavy crude but again, is that relevant? And if your Mauser system rifle is 'stove piping' as you say, I'd suggest it's malfunctioning (as all mechanical things tend to do sooner or later) and in need of some urgent remedial action. Properly functioning Mauser action rifles don't stove pipe in my experience.

As an IT guy I'm sure you'd agree that, as mentioned above, mechanical systems will usually fail sooner or later. And as a spring operated button ejector is inherently more prone to failure (on a number of grounds) than a non-mechanical fixed blade, why would you knowingly put your life on the line and elect to take the former over the latter. Similarly, we know that short-stroking can leave you with a completely inoperable firearm, often at the most inopportune moment. So again, why would you knowingly take that risk when you don't have too? The problem of short stroking was solved for the most part with the development of the non-rotating claw extractor so why not take advantage of the development and potentially save your own life? Sure, you can hunt DG with a flintlock if you want and you may well get away with it too, if you keep the thing well maintained etc, BUT, the potential for system failure is even higher than the potential cock-ups that could happen with a push feed action [although perhaps only marginally so

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And finally, as you allude in your comment, the push feed action has one major advantage and that is cost. I don't know what Remington spend to produce their push feed actions but I'd guess something less than a third of what it costs to produce a Mauser clone. That, if I'm correct, is a significant difference, if you're just using the rifle to shoot vermin but probably worth every penny when hunting DG under conditions of great emotional stress. But as you say, you can't fix stupid.