I wouldn't care much about 161e warranty for $50-60 price.
Got anything close to 161e feature wise, better protection around $100?
There is no free lunch. The Fluke 101 is the strict low end of Fluke with robustness but zero features (and quality control issues in my experience). Brymen/Greenlee is what you are going to find with reasonable robustness and more features at the same price range (also Klein). The newer Uni-T models seem to have reasonable mechanical robustness, but electrically they are not as good.
If not, would 161e be safe while working on 240v 3 phase machines? I would mod it to make it more robust but not electrical engineer, and I know it's not allowed to ask for help with that here sadly.
This is a question that can be approached from many angles.
From a multimeter perspective, the UT161E, the UT61E+ and many others (even the throwaways M830B-clones) will probably be just fine working on such systems during normal operation - they can withstand 240V just fine. However, if an unexpected event happens (high energy transients, for example) the chances of the cheaper equipment to survive are much smaller than a more robust one.
From the perspective of the operator and since you asked about "safety", Joe's tests cannot help you. Sure, a meter that survives a low energy transient has a higher probability of containing the damage of a high energy transient, but without testing it is a very far fetched claim. To verify this, a very high energy transient would have to be applied (something that the independent agencies claim to test to the full extent) and the meter would have to either (1) survive without damage or (2) die but in a controlled way to not harm the operator. In this particular scenario, I can tell for sure the M830B throwaways will be much less safe than anything else on the marketplace and will probably blow in your hands - an Uni-T meter would be less robust than a Fluke/Brymen/Klein, but without testing no one can really know.
The suggestion for more than one multimeter is very sound, but only if you are interested in investing twice your lowball budget. In this case, you can have the best of both worlds: the extra features of the Uni-T for the bench and the safety of a simpler robust model for the field.