Hey! I'm the same when it comes to mangos! Wow, haven't really met another. For me it's only when the mango skin comes in contact with my mouth. So I wash the fruit with dish soap to remove excess oils, then peel the mango. I also don't eat the flesh too close to the skin and use extra chapstick before I eat. Sometimes it works. When it doesn't, my lips feel like sandpaper for a week. I was researching it and it's a pretty rare sensitivity so lucky us. I also read a paper that claimed if we had mangos before we came in contact with poison ivy, we wouldn't have had the mango sensitivity later on in life. So if you have kids, make them eat mango!
Anyway, I thought of another tree. Jujube trees. They love the sun and are very drought tolerant/cold hardy. Downside they are deciduous.