I actually question the value of the grace period. Once you've hit the answer button, any further edits should be tracked separately from the initial submission. This should eliminate garbage "first post" answers that are edited later on purpose.
I only see why someone could consider this problem when others do that, if that someone is mostly concerned with their rep. That's fine for their personal concerns, but the site in itself shouldn't be concerned with this, the site's concern should be to produce great answers.
If a first, suboptimal answer, followed by incremental edits, leads to a great answer — what does it matter whether this incremental progress was recorded for the first 5mins or not?
IOW: I see no reason to change anything.
As an outcome of the comment discussion below, let me take up the cudgels for the current state:
The feature where changes are coalesced is there for a reason: I do not want to see individually every typo-fixing change some author does, when I look at what changed. I want to see those changes coalesced, because it's much easier to look at them that way.
If you make me look at every typo someone fixes in their answer/question individually, the very next thing I will ask for here is a feature where I can compare rev X to rev Y, where Y != X+1, because otherwise it's impossible to get an overview of what someone changed in half a dozen quick edits.
And, FWIW, I see no reason to be logically inconsistent in that regard between the first edit (the one that creates the answer/question), and the following ones. To the contrary, since a question or an answer is changing a lot more in the beginning, when the author sees all their little mistakes and inconsistencies, and when commentators point out even more of them. The beginning of an answer/question is exactly when coalescing is needed most.
So please leave this as it is. It is a helpful UX feature that would be missed. Or if you indeed must change this, then please at the least give me the option to look at the coalesced changes.
Now, if there is indeed a problem with users stealing other users' answers, and if this indeed makes those other users angry to the point where it damages the sites goal to produce outstanding answers, then let us tackle this. Allowing to view the changes uncoalesced at least for mods would probably do.
Also, if many users indeed see it as a problem that other users sneak in dummy answers first, in order to be the FGITW, then let's tackle the FGITW problem. Let's just remove the FGIW badgeFGIW badge, or at least, change it so that it honors answers that gain 10 upvotes without being edited once (which, IMO, leaves the badge's spirit, while encouraging the exact opposite behavior).
Pushing people to aim more for the site's goal (producing outstanding answers), rather than their personal goal (accumulating outstanding rep), is a good thing.