Actually, I think it's best to place the beginning of Movie 15 in January, AGE 779. Freeza takes four months to surpass everyone and goes to Earth in July. We know there is a six-month timeskip because Piccolo said so (the Dragon Balls were used six months ago). The other two months left I like to think is the time Freeza took to arrive on Earth.
With the later part of Movie 15 taking place in July, I would place the Champa tournament in August. I like to give characters time to breathe a little (this is where I change in order to cram more stories and timeskips should they appear).
If I place the Champa tournament in August AGE 779, then the Universe Survival saga must take place in August AGE 780 or after that (for the reason you yourself mentioned already).
With Universe Survival saga taking place in August, I would place Moro saga in September AGE 780. And that two-month timeskip during that saga get us to November of that same year.
So you see, we can't even afford to have another two-month timeskip anymore. If we do, I'll have to forget my preference to give characters some time to live their lives and the gap between the sagas would have to be shorter. All in order to cram more unnecessary stories and to avoid the problem with Bulma's line.
Everything about AGES is important (to me at least), it's a way for we (well, me) to keep track of things.