When the verb is simply "get together" (in any tense and not followed by "with [someone]"),
the subject must be plural, so 1. is impossible. 2. is good. "time when" is better than "time that", in my opinion.
3. and 4. are both correct. Neither is better.
You simply have to say 3. when you mean 3. and say 4. when you mean 4!
3. concentrates on the description of what will be happening. It gives a more intimate feeling. It suggests a sort of pleasant activity in this particular case.
4. concentrates on the mechanics of the schedule -- what will happen and when. Because of the poetic nature of "same bright moon" 4. may be (very slightly) less appropriate, depending on your purposes.