Question is, how do they define "strictly gradual"? For example if right view/right intention already come into being, going with the "strictly gradual" process, does that mean one should hold off on right speech for the next month
Gradual - means you pay special attention and direct most of your efforts (most - but not all) to a particular factor. 1st come Views - you have to understand things first, this is where you should put your efforts from the very start. You can meditate, give dana, try to be gentle, etc etc etc - but Views is something which requires all your attention, when you are on the start. This is the most important thing right now. When you see your views are correct and strong enough, you go to intentions, that is, right, skillful desires in life. You spend most of time on changing your real life vectors - that what it is. When you see that it done, you pay special attention to morality in its three forms - bodily, verbal, mental. After that you pay more attention to developing good qualities and removing bad. When this is done to a great extent, you pay special attention to mindfulness development, and when it is developed to a good degree, it will naturally lead to jhana, which you develop as the end of the path. Developed jhanas together with right views will lead to nibbana. This is what is meant by gradual.
Again, on paper everything looks smooth and clear, but in real life this doesn't happen. Delusion and other defilements play a great role in our practice too, unfortunately. So most of us go this Path by trials and errors. For example, one may spend years on "this/that" buddhist practice and after that realize that he doesn't actually believe in all this stuff, and quit, forever. He thought that, probably, he had 1st path factor developed. But that was a delusion.