Linsey....I could eat almost an unlimited amount of really low-carb veggies (broccoli, salad greens, etc.) and did not even count the calories...and continued to spill ketones and to lose weight. I didn't even bother counting the carbs of these veggies....the one in the first group of the lowest low-carb veggies in the book.
I also put lots of butter on my cooked veggies...to get the fat in. Plus it tasted better and kept me full much longer. And yes, I would absolutely switch to real butter.
You don't have to eat butter AND mayonnaise.....if you don't really like mayo...just make sure you put plenty of butter on items or cook with butter quite often. It can be AND or OR....doesn't have to necessarily be both...but for some reason....I found both butter and mayo to almost be a different type of fat from say, meat (dark meat), etc. While yes, I could eat those items....I seemed to need lots of either butter and/or mayo to maintain consistent loss (no matter how much of the other fatty foods I ate).
It's weird when we do Atkins. Many of us have to over-ride years worth of diet advice....stick to white meat only, avoid real butter, etc. It's a whole different way of eating....where fat is good and carbs are the problem. But as you lose weight....it will gradually make total sense to you....and you will realize that most of our entrenched dietary beliefs are way off the mark.