Oren wrote:

Drill a small hole in the gutter in the low point where water
is pooling. This will give the stagnant water somewhere to go
(ie - down)

Having a weep hole above the front entrance?

OP wrote:

"...the low spot is right over the front door."

Well, if the water is collecting over a 20-foot length, then putting the
hole just adjacent to the door (and not directly over the door) should
be possible. Note that when it's raining or just after a rain for an
hour or so, you're not likely to be inconvienenced by having a gallon or
two of water drain onto the ground in front of (or beside) your front
door area.

I did this on my house (drilled a small hole in the gutter) to drain a
low point, but this was over-top another roof section so that water
simply fell and got collected by a another gutter section below it.

The OP also says this:

about 3/4" / 1cm at deepest point

I've seen in old discussions here advice about pulling the
gutter and remounting it, but I don't see how that's
feasible. We're talking about moving a gutter less than
the diameter of the nail/pin that holds it in place

If the water depth is 3/4", then you need to move the low point up by at
least that amount to prevent a low spot from forming. Way more than
"the diameter of the nail holding it in place".

and it's not like one can just move the nail/pin to
the left or right, yes?

Normally the gutter is nailed through the face board and into the rafter
ends directly behind it, which are spaced every 18 to 24".

But the reality is that putting a 1" screw with a wide pan head (ie -
wafer-board screws) through the back wall of the gutter and into the
faceboard every couple of feet is all you really need. The front edge
of the gutter doesn't really need to be supported at every rafter joint
like it normally is by the hangers. You never have so much of a load on
the gutter that requires that sort of bracing.