First, hello Greg and welcome to The Shave Den.
Next, don't be worried.
Lots of guys have the problems you are having, and they get it figured out.
You will too.
You made a pretty good write up, with enough detail so that we can probably help.
Some things that you said that concern me are:
Ok. This sounds to me like that even after you shave, there is enough hair above the skin surface to grab with tweezers.
So, you're cutting the whisker off, but maybe not right down to the skin surface.
This is a problem. You see, what soap does is bond with oil and dirt and suspend them in the lather
so that they can be rinsed away. For shaving, we want the natural oil that is in the whisker (making it soft and limber)
to be drawn out so the whisker will become less "wet noodle" like, and stand up. This will let the blade slice it off cleanly right at the skin
surface, or very slightly below. You are a young guy, and your whiskers are likely fairly fine. Also, you probably have
plenty of natural skin oil. To combat these two things, I think you need a good shaving soap, and a good brush to apply it with.
(If you don't have a brush or a shaving soap, PM me.)
and
Oh my.

You may be dulling the blade(s) by doing this, and that may be what is making the razor feel "smoother".
Instead of pressing the razor on a towel, just give it a couple of brisk shakes to remove the excess water.
Hmmm......
So if I'm reading that correctly, the downward pass really isn't cutting anything at all.
It's really the ATG (against the grain) pass that is cutting.
I'm convinced.
Your prep in the moustache area needs some serious work. (Shaving soap and a brush)
You may also need to put a new cartridge in Harry's machine. (you should be cutting on the WTG pass)
No more towel drying. Make sure the blades only touch your face, and nothing else.
Above all, hang in there Greg.

Things are going to improve.
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