Think of it less as an actual particle that has a speed and position at a certain time, and more that "speed", or "position" are just the results of measurement

Think of it less as an actual particle that has a speed and position at a certain time, and more that "speed", or "position" are just the results of measurements that are made. The electron is a cloudy, blurry mess, yet if you measure its position, you'll find it is in a certain location, but that's all it means. It doesn't mean it "was there" before the measurement! Likewise, if you measure its speed, you'll likewise get a precise speed measurement, but it doesn't mean it had that speed before the measurement! Or that it was actually speeding from any point x to a point y. So, while the measurements work, what breaks down are the regular common sense implications that the measurements normally imply.