I know that there was resistance to tracking partially-used clips, so the same would probably hold here.
However...
Perhaps it's not as tough as they're thinking. Whatever variable stores how many you have of something, change it from an int to a float. Look for all instances of that variable and change them from 'foo' to 'floor(foo+0.001)' (the plus is to eliminate floating point rounding errors). Now you can keep track of fractional clips. Since you're using floor in most places, you won't see any ammo that doesn't fully fill up a clip -- but whenever your fractional clips add up to enough, you'll end up with another clip.
That would be a first step, of course. The next step would be to make the hidden, partially filled clip visible and usable (perhaps turn it red to show that it's not full). This would be more difficult; however, you can still do the first step and get part of the goal accomplished without doing the second step.
Just one possible way (among many) to approach the issue.
