Will it be grammatically correct to say "How long more must I wait?" instead of "How much longer must I wait?". Do they convey the same meaning and stress?
I just wish to avoid the most common phrase.
Are there any more examples?
"How long more" is not grammatical English. You can say, "How many more," if you specify a countable unit of time, or, "How much more," if talking about (uncountable) time in general. For example:
How many more days must I wait before they let me know if I've been accepted?
After fertilizing, how much more time must I wait before planting new seedlings?
However, these expressions are not as common or natural as, "How much longer must I ..." They are common in other contexts:
How many more days until graduation?
Traveling for work, how much time do you get to spend with your family?