In my experience it was not that hard (as far as 25 year old games go) to get running on a Windows 10 system, which is what I played MC1 on and made Mantis on. I wrote down the steps I used[1] but there are alternative approaches using e.g., dgVoodoo which are not hard to find if you search for them. As far as I'm aware there's no need to use a retro system to reliably run MC1.
If you are for some reason intent on playing MC1 on a retro rather than modern system, Mantis is just a glorified automated hex editor and you can byte-for-byte replicate what it does to the game exe by copy-pasting the hex edits which are already outlined in the OP (for the bug fixes) and elsewhere (for the rest of what Mantis does).
I was just noticing that there was a whole lot of work fixing these minor bugs, and then went all lazy writing the patch... Or maybe I was spoiled by decades of scene patches, cracks and tiny demos with chiptune music and funny graphics.
There is a certain irony I guess, but in my eyes the "patch" is the hex edits, not Mantis. If I had published these fixes but never gone back and made Mantis, I would still have considered the work "complete".
Mantis was made nearly one month after the actual patching was done partly as an excuse to test out a few things like the build settings available in newer .NET releases (e.g., framework-dependent vs self-contained build with trimming, JIT vs AoT vs ReadyToRun compilation). It wasn't really laziness to target .NET 8 because exploring those build options made it take longer than just building using e.g., .NET Framework since Mantis is so basic. As I said, glorified automated hex editor.
So, it won't work on the same retro PC as the game.