So, you're in one of two situations if you're getting leetcoded vs. let in through the side door at a company (i.e. through your network: the red carpet)
1. You're a newgrad. You have no work history, but you do have a lot of time on your hands and a desire to prove yourself. Go study leetcode and prove how awesome you are.
2. You're a senior engineer who has a small network (not a dig, lots of great developers are introverted and have small networks, myself included). In this case, it sucks but... just practice leetcode. Don't worry, the fact that you're a good engineer means you'll pick it up quickly. It's not the same skill as professional software development, but there's a ton of skill transfer, and it might even be a little fun.
Time crunch, test anxiety etc, those can be overcome by practicing. A lot of times really smart people are averse to practicing since they never had to do it in school. But, I'm telling you, any smart dev can learn to leetcode well while being timed. It'll be fine