Very enjoyable viewing, well done! I've got that lens and haven't used it much lately, this make me want to, but I know it's the skill, not the lens.

I'm late but I think you have some good answers, the moon does move a lot (we're moving too) and it will seem to move in faster when low in the sky since it is closer. And you do have the atmosphere to shoots through which can distort it a little, but also gives those great orange colors. I really like your second shot. Sometimes you cannot help but capture a haze, I think it comes from moisture in the air but I'm not certain, and also it can come from overexposure. On that pic you might try lowering the exposure and then boosting fill light. It probably won't get rid of the haze around the moon, but it might lower the amount.

I try to shoot the full moon each month at moonrise, but usually the clouds obscure it. Usually the full moon rises within an hour of sunset (at least where I live in Ohio) so there is still some light, and it sometimes makes it a little easier to get better exposure since there is not as much light difference when everything is black, still you have just a short window to work in. The shot below had a little more light to work in, so it's 3.2 seconds, f8. ISO 100, you still have a halo, it was a little hazy but the moon had to be overexposed to catch the barn. And the second with even more light shows a pretty clear moon at 1/20 second,

Serene Moon by Tom Ramsey, on Flickr


Red Barn by Tom Ramsey, on Flickr

It could be aperture block failure, if so it needs to go in for repair. Do a search on Google, you can find out a lot more about the symptoms.