When I did this the transformer was out of the microwave. I put the meter on the ground, used alligator clips to attach it and stood back away so no problem. There is a way to do it safely. People with children should encourage their kids to not experiment with high voltage unless supervised.
Although a hard fault to ground on the secondary will increase thermal losses on the transformer, it will still output a significant fraction of the 1000VA (2kV/.5A) - it will not go easy on a DMM that happens to be on the way, especially if you depend on its quality (or the lack thereof).
That said, in my experience with the levels you are working, only poorly maintained or super low-quality DMMs like the ones you have been using will effectively be in danger of ejecting matter outside of their enclosure - I would be either behind a shield or at a very conservative distance. Anything with a decent enclosure (or even the rubber holster) will help contain the bang. Any issues with the voltage range or accidentally leaving the switch on the mA range (fused) of the DT830 will potentially be less consequential than plugging such voltage to the 10A unfused terminal.
That only talks about damage to the equipment and not to the most significant element in the room - YOU.
If you look at Joe's latest video about the Fluke 87V, you will see how it can withstand 1.6kV continuous DC on its voltage range without any perceptible change in its characteristics. However, this is a well built DMM with a very decent enclosure - I don't think it would survive a 2kV jolt as gracefully as it did, but I also don't think you would be at risk of it exploding in your hand/face as well.
Taking this into consideration, I think Fungus' suggestion about the Fluke 101 is excellent, but unfortunately you are already having issues with either Aduana México ó Correos de México with cheaper Anengs - imagine what they would do to a Fluke!
(I know very well what it is to deal with similar corrupt systems).