A V-bit is a much better choice for strength, but your problem is too fast of a feed rate. If you broke a 1/8th bit, it is pretty clear to me that you are going too deep and too fast. I know it takes a LOT longer to do things, but if you want it to work, you need to slow down. It isn’t about the speed of the machine and how fast you can expect to get it done.
Listen to the machine, and watch the bit. My machine can do 2,000mm/m, but I can rarely go that fast. Any bit that has a smaller tip than the shaft should be slowed down by half (or more) per half a unit. For example, I can do a through-cut with a 1/4" straight bit at 2,000mm/m, but a 1/8" bit can’t be more than 1,000mm/m (I go about 750mm/m), and at 1/16" I am more like 300mm/m or less. At 1/32", I would be pushing my luck at 100mm/m.
I do use v-bits similar to what you have posted, and they work great and are strong. That does look like a good choice. But reduce your feed rate. With a bit like that, I can do maybe 500 to 750mm/m on a softer wood, and 350mm/m or less on a hard wood.
Your machine is different than mine, and maybe you can go more. I’m just saying what works for me. Listen to the sounds that it makes, and watch what the bit is doing. You want it to be smooth, not struggling.
If you are using Easel to carve, you can change the speed on the fly up in the toolbar. Make it go faster or slower to find the sweet spot. Otherwise, just be patient and wait. Quality does take time.