Okay.  I just saw a picture of one, and it kind of reminds me of an Olivetti Studio typewriter I once had (I am not sure if it was a 44).  But I can tell you that I had to unscrew the left platen knob in the reverse direction because the threads are left-handed--just like the Underwood New Style 150 all the way to the Type-Master machines.  I am sort of half-guessing here, but what I saw was familiar, and I remember I had to unscrew the left-hand platen knob left-handed.  Try it, and let me know how you come out.

Oh well, you can't win 'em all.  Wish I had that sucker here--I'd figure it out.

What you may try before removing the entire carriage is to see if there are any setscrews on the shaft anywhere--the platen knob.  You may have to look inside the left carriage panel, though it looks pretty thick.  Also, I'd look on line to see if there are any repair manuals at least addressing the removal of the platen.  Carriage removal--especially if there are loose bearings involved (like in an upright Royal)--is tricky business.  Anyway, try this.  It is a more common way for platens to be fastened in--at least in older typewriters.  Also, if you can unscrew the setscrews that may be in the platen knob, you might see if you can do the same to the right hand side on the platen itself on its shaft.  It may be held in placed by a long rod like old Royal uprights and Royal portables.  Underwood old style (like the number 5) has two short rods on either side, so you have to remove the setscrews on the platen shaft only.  Underwood new styles, including the Touch-Master series, just flip up the sides and life 'er out.  Anyway, try this one other method.  In the meantime, I'm going to see what I can on one of my own Olivettis (it's a Sears disguise, and it's a dinky little thing, but there may be similarities).  Good luck, and if I can get what I find to you before your planned surgery on your machine, I will try to get it to you quickly.

The Plot Thickens...

In case anyone is still interested:

I looked at another Underwood 21 (Made in Italy) today. The rod that goes from the left knob into the platen screws out counterclockwise - just as you suggested!

However, it looks really different from the Olivetti-Underwood 21 (Made in Spain) that I have been struggling with. Grey metal instead of black. A flat surface around the hole in the platen instead of a kind of raised nipple. Very strange. I'm going to tinker with it a little again tonight and see whether maybe getting some mineral spirits or 3 in 1 oil down into the rim where the spindle goes into the platen loosens it up. I am not hopeful because I really put a LOT of force on it last time. I was actually afraid of snapping off the right handle or warping the platen drum (or whatver you call the metal cylinder that the rubber cylinder goes around).

Neither mineral spirits nor 3 in 1 oil did anything. It isn't budging.

To cheer myself up, I spent the rest of the evening cleaning out a very dusty and gummy but otherwise excellent Brother Signature 440T that my lovely wife picked up at a thrift store for $15 the other day. Got it working perfectly and shined up the high-tech "Cycolac" (plastic) so that it looks about as good as new.