Dictionaries lead me to understand 快乐 as happy. Whereas 喜乐 as delighted, happiness, joy. In English joy denotes a stronger, deeper emotion. Is the difference in meanings of 快乐 and 喜乐 great enough to express the same contrast?
I think what you mean is 喜悦 not 喜乐 though 乐 can also be pronounced as yuè . This is how I differentiate the two:
快乐 is more obvious than 喜悦.
You can pretend to be 乐, but you can hardly pretend to be 喜. You can easily find someone 乐 but you cannot find someone 喜. That's why this word is seldom used. Here's a word 喜欢 which means 'like'. 欢 is happier than 乐, you may dance, sing and jump. Thus this word means "when you see this, you are 喜 and 欢", so this word means 'like'. In the ancient time, 喜欢 can also be written as 欢喜, but in modern Chinese 欢喜 only refers to an emotion.
快乐 is the same as 乐, while 喜乐 is happiness, joy.
When 喜 and 乐 are together, you're REALLY happy (not only 喜 but also 乐), you are laughing loudly, or other actions, for example, your emotion after you win a lottery ($999999999999999).
I don't agree that 喜乐 is 喜悦, because 乐 refers to music when 乐 is pronounced as yue4.