You're right, me either. If you say it that way 很快乐认识你or 祝你生日高兴，it makes me want to correct you immediately! haha...Just wanna say these two sentence are pretty settled, if you change to another way will makes people feel weird. And I think "快乐“ is a word saying you have a longer/deeper pleasure compare to the word "高兴”, that might explain why "快乐“ is more often used in books. To me, "快乐” is pretty similar to the word"幸福“（it means happiness）,except I feel more peaceful in "幸福” than in "快乐“。

you can only say很高兴认识你 and 祝你生日快乐 。高兴stand for a short time, like few hours, few days,months. 快乐is for a long time, maybe whole year, the childhood, even whole life. 高兴is used in oral English more times .

How can I get into contact with you? I would like to help you with English. :) In return could you help me with Russian? Thanks. :)

*I've NEVER seen and never heard