Complete success! I threw out the solid center pin and stuck a length of Bic pen down inside the valve stem, after drilling 8 holes in the piece of Bic pen for better water flow, and now (after some careful trimming of the pen piece to the proper length) I have a fully functional QFD that works just like the original! (The piece of Bic pen depresses the check valve on the Monster and the homemade check valve at the same time, since they are pushing against each other on each end of the pen piece - try sticking a Bic pen shaft [after removing the end of the pen] in your Soaker's filler nozzle and you'll see what I mean)
I attach it to the hose, turn on the pressure, and no leaks/drips. I shove the nozzle of the Monster in there, it makes a satisfying faucet-like water-flowing sound, and it fills in around 3-4 seconds (probably closer to 3) - I'm assuming it's filled when it makes that whining noise, which I'm guessing is the overpressure safety valve squealing. I remove the nozzle, and the only little bit of water that comes out is what was in between the valve stem and the nozzle (i.e. very little).
I will try to post pics (and a link to a YouTube video proving it works, if desired, and maybe a diagram). This thing works so well I'm wondering how close mine is to the original design of the Monster QFD.
Thanks for all your help - once I saw that makeshift check valve, I knew what had to be done

I'm actually amazed it was this easy - I read a lot of inconclusive posts about people wanting to buy or build on of these before moaning about it myself
Now I just need to build a ground-mount for it - I now realize there's a reason those original QFD's mount on the ground - so you don't wear out your arm holding the QFD against the fill nozzle.
-Jon