The No.31 has a different handle shape than the 127. I don't have direct personal experience with those models. The 157 is a more forward-weighted chopping design.
I think you'd save yourself a lot of headache and analysis paralysis by just buying several machetes of different patterns and getting some field experience with them. They're economical enough that there's no harm in buying multiples to build up your hands-on knowledge and ability to read a pattern and its suitability for your contexts. A lot of these questions, while simple at surface level, are beyond what can be meaningfully answered concisely and would require a lot of typing for something that's made readily apparent with just a little field time with a handful of different styles to play around with. Most of these designs will get your tasks done and the most important thing is if they're a light pattern, a medium pattern, or a heavy pattern, and if they're long or short. The further distinction between them gets down to hair-splitting that, while definitely meaningful for folks using them for more than an hour at a time, are VERY laborious to communicate through written word out of context.