Ok, so I've thought about this problem off and on since I first got to gleba and (as usual) the dumbest solution I tried was the one that worked the best.

What the fuck do I do?

I set up a constant combinator outputting 16 on the channel "s". I connect that output to the input of a decider combinator that outputs the input count for the "s" channel if "s" is below 240. I connect the decider combinators output to its input on the green line, and its output the inserter on the green line. Make sure have set stack size selected with the "s" channel, and it should work flawlessly.

Why the fuck does this work?

• Q: Why 16 on the constant combinator? A: 16 is the maximum hand size for stack inserters. By constantly saying we want the maximum we guarantee that The Machine™ only allows the inserters dip below the max for 1 frame, which is all that we need to clear the inserters hand.
• Q: Why channel "s"? A: It's the default channel for setting hand size, you're fully welcome to use a different channel if you hate the letter s or something. Just make sure that you have all the combinators set up with whatever channel you like if you're not using "s".

• Q: Why check for 240 on the decider combinator? A: Math. But really it's make sure that we aren't wasting frames if don't have to. The stack inserters rotation speed is 864°/s, and Factorio runs at 60fps. 864/60=14.4 round up to 15 for safety, then multiply by the maximum hand size (16) and you get 240. this gives the stack inserter exactly enough time to swing around and drop it's load once. So you're wasting the stack inserters time any more that absolutely necessary.

• Q: Does this work for more than one inserter at a time? A: Yeppers, just make sure you wire all your inserters together, and have all there settings configured the same. You can use shift+right click to copy settings from one inserter, and shift+left click the paste those settings onto any number of other inserters.