I made panels just like you are saying when we lived in Michigan (~30 years ago). I made a wooden frame and covered both sides with heat shrink plastic and used cheap foam gasket on the sides to "press fit" it into the window frame.
The windows were already double pane, but the improvement was remarkable.
Since my first attempt, I learned that a very thin layer of air is just as good as a larger layer as the thin air layer attenuates convective flow. Convective flow is what kills the insulation value.
So, I tried building very thin panels with only 1/4 inch (4-5 mm) spacing. My problem was that the frame was not strong enough and would warp when I heat shrank the plastic. Thus it would not seal well in the window.
Argon has pros and cons. It eventually leaks out - even in expensive Pella and Marvin windows. The increase in R value with argon is real. A friend sealed his frames really well and filled each with dry nitrogen. I knew that nitrogen worked as in there was absolutely no frost at the bottom of the insert on sub zero mornings. But after a few months, frost began to appear (as the dry nitrogen leached out).
I was amazed how quickly these frame inserts could be built. I used a simple miter box, some hard wood base materials (got broken ones from hardware store they were throwing out), a staple gun, a roill of foam gasket material and the film (the most expensive part).
It took a bit of experimentation to get the measurements down as the foam must compress just a certain amount. Too much and it doesn't fit in. Too loose and the panels literally blow out in a wind. On some windows I had to use foil tape to keep the panels in
.
In our bedroom, we actually used "bubble wrap" inside the frame and it outperformed everything.
Interestingly, the windows worked very well in summer as well.
Let us know how this works for you.
Steve