I'm so sorry for your loss.
I have written and delivered several eulogies, most recently for my grandfather.
You really do need to go slowly when speaking, and type your final version out in a large, clear font. A little tip for me was to have "marker" points in case I got lost. For me, it helps to look out into the room, as you do when speaking to a large audience, but not make direct eye contact with anyone, as that is where I have difficulty with not falling apart.
Brainstorming will help you write it - I often start by brainstorming a list of words that describe the person best. Then when you read them to yourself, you'll likely think of special anecdotes and memories that show why they had that characteristic.
It may sound silly, but I've found it helpful to play music the person liked while I'm doing this. You're trying to encapsulate their life - what they did, what was important to them, what they did that mattered and will live on even after they are gone. How they impacted you personally, or added to your family life is a good place to work from.
Going through any photos you have helps if the memory thing is sort of "blocked" with emotion right now.
Also, expect other people to cry when you are talking. This sounds simple but it can really throw you the first time if you aren't ready for it.
Hope this helps a bit. FWIW, I understand what you are saying in that I also have an extensive public speaking background and it does not help at all because of the emotion involved.