Hey fellas,
I do not profess to be a red dot expert however I have considerable experience using red dot sights on medium & large bore rifles.
My favourite system is the Aimpoint 34L which is a larger set up like a light scope. I have used this on many running pigs with my 9.3x62 where it is incredibly instinctive in this situation. I have shot 1.0" groups using SSAA targets where I can use the target to centralise the 2.0 MOA dot. I found the lack of movement amplification due to no magnification very calming & I love watching the dust fly on impact with the two eyes open process. Bigger game is a piece of cake. A commitment to dry firing certainly helped me develop the necessary skills pretty quickly. I also have considerable open sights practice which is similar. I swap out this system with a traditional scope if longer shots are the norm in open country.
I intended to use this Aimpoint on my .416 Taylor but now favour an Aimpoint Micro H2 so that I can keep the rifle weight to about 8.5lbs, no trouble getting all bullets to touch at 50m using the same technique described above. Only a couple of easy shots on game so far but I think it works fine.(Similar performance to my Rechnagel sights). The H2 is a little less instinctive compared to the the 34L however better than the alternative sighting arrangements.
Recently I used a cheaper Crown red dot 3MOA to cull plenty of donkeys & brumbies on my cheap Remington M78 .308W, shots out to 200m not a problem. Running shots were a dream although occasional back up shots were needed.

Hope this helps!