This probably isn't very helpful, but I've found that it does work:
Research.
Get as much hard science data on it as possible.
Correlate it with understandable explanations.
Put the two together and print them out. With pictures/illustrations if possible.
Work out a diagram/illustration of what YOU plan to do.-Since permaculture is open to easy design try to use shapes that work around/with their mindset/aesthetics. (For instance, my peach guild is going to be a tidy circle, and while everything in it will work together and be edible, it is also going to be appealing to the eye, something that most permaculturists don't have to worry about quite as much in planning. No overgrown tangles of shrubbery or high-growing herbs there.) Permaculture is flexible in design. Design something that is both useful to the plants and useful/workable for you and your friend. There's nothing saying you can't design rows, or S-rows, into your plan. Try to find catch crops that have a secondary use that is sufficient that your friend will recognize it and feel comfortable with them.
Another thing you could try is designing two areas. One in a traditional design, that will act as a control. One as a permaculture design (again, you might try for tidier overall design than the norm [or norm for what I've seen posted]) as an 'experimental area' to prove that over time it has its worth over traditional design.
Remember, your friend is going to appreciate beauty/tidiness and functionality most, so do exhaustive research to find the plants that will work best. Don't go for the first solution or the most popular
permie plants. Go for what will work best for you, your friends, and your area. (For instance, you could use a catch crop that doubles as cut flowers that can be sold at the co-op.) Border areas such as you speak of are good for appealing designs, especially for a farm that produces locally and needs areas that photograph well to draw approval from the customer base. (Photos posted in store, sort of thing.)-
Give them these as you explain.
Explain in terms of strict functionality and science as much as possible. Also note the eye-appeal, and lower amount of work designed into your plan.
Also, ask them often if they have any imput or advice. They might do traditional farming, but that doesn't mean they won't have good advice, and they'll be less likely to blow you off if they don't feel that you are ignoring their experience. Present it as working with traditional methods, complementing them, not against them, trying to push them out entirely. As you noted,
"My theory is better than your experience." is one of the fastest ways to set up someone's hackles and make them work against you rather than being open to your ideas.
Don't expect a total conversion of attitude, even if they are impressed with permaculture. You probably won't be able to prove your point and get the land entirely converted to permaculture within five years. I don't feel that is even realistic. Trees and bushes take time/several years to grow and produce. And one or two years isn't going to prove much unless the difference in production AND work is dramatically in favor of your permie area.