I try my hardest, and in every way I can think of, including planning out the conversation ahead of time, to avoid conflict but it doesn't work. To avoid conflict, I simply need to not have the conversation because he gets so uptight. He literally starts waiving his hands and you can see his body language change and perspiring over the stress...not sure exactly what an anxiety attack entails, but he certainly doesn't handle stress very well. I've noticed this while simply performing a task around the house as well. He gets stressed very easily.
When you say you have a need for that convo, are you really wanting to get your message across or are you wanting to hear his? Are you seeking to negotiate something?
John Gottman talks about something he calls "harsh start ups." Men's blood pressure raises instantly when they hear something like "we need to talk." It's literally THAT automatic! You might be saying "We need to talk to tell him he's won the lottery and he'll have that same reaction because he's conditioned to think defensively when he hears ANYthing that indicates criticism/confrontation MAY be coming.
So harsh start ups are a problem, and rehearsing won't do a thing if the approach doesn't eliminate that initial response. Some possible ways to introduce topics that can eliminate that harsh start up is to deflect attention from you and him when you do. For instance, you can ask him his opinion about something you read that touches on something similar to what you'd like to talk about. You can mention a friend who is going through something similar and give your opinion and listen for his response. But what's necessary throughout this, as mentioned above, is that he must feel safe. If he anticipates any judgment or disagreement, he will enter a fight-or-flight state of mind, and I can tell you from long experience: As emotions increase, logic decreases.
I asked what your goal for the conversations is because once you understand about harsh starts, you can use your goal to consider ways to soften things and help him feel safer.
If you just want him to understand and validate you, maybe he'd feel ok with it if you set a 15-minute time limit and explain up front that you're not asking him to fix anything but just that you need to unload to a friendly ear.
If you are wanting to understand his views on something, you must be able to listen without a conversation. This means watching for his reactions and becoming intimate with his body language. You already know that when his arms start waving and his tone/volume/pace of speech changes, that he's signalling distress. How does he signal confusion? Unhappiness? Contentment? Once you learn to recognize these things, it may help to formulate his emotions into a question: "I thought you seemed unhappy when I said XYZ. Is there something you'd like to see instead?" You must also learn not to use blame or criticism. EVER. There simply is no room for that in a healthy relationship and even less than zero with a guy like yours. He'll suffer silently until one day he's gone and you have no idea why he left.
Negotiating with someone like him is very challenging. After all, his entire aim is to AVOID conflict. IF he comes to see you as a partner and not an opponent, it may help. As I said, I've never dealt with such a high degree of this, but I can tell you I've often been seen as an aggressive, demanding woman. Something I've learned to do in general but especially with people I know are uncomfortable with confrontation is to use statements designed to set them at ease and remind us both of our common goals:
"I know this is uncomfortable, but we are a team. I believe in you and I believe we'll be able to find a solution together."
"I am not your enemy. Please don't perceive me as one."
"I know that this is horrible for you. What's one thing I can do that would make it easier for you to have this conversation?"
Finally, I make it a point to be cooperative on most things with my partner, and I use this to calm down situations. I don't struggle for control/power any longer because it's rarely worth it. Instead, I let him choose what we do in our free time, how we do things, which route we take, and all these "little" decisions that arise every day. When something important to me comes up and it's only minimally important to him, I've said, "You know that I give you your way as much as I'm able, but on *this* matter, I'd like to have my way with your blessing."