Misaligned paths when outlining in Illustrator

I created the font design in Illustrator and copied them into Glyphs to make my font. When I create outlines of the font in Illustrator, the paths seem to be a bit offset when I compare it back to the original design.
(I’m exporting as .otf)

Black is the original design
Green is the shape I get when I copied a randomly sized shape into Glyphs (ie height 1000.XXXpt rather than 1000pt exactly)
Pink is the shape I get when I copied a 1040pt height shape into Glyphs

I understand a small bit of offsetting as I’m doing the base design in Illustrator rather than Glyphs, but you can see how the lines are not even straight, which I find problematic.
Is there a way to fix this?

When you copy outlines from Illustrator, all coordinates are rounded. That can lead to small deviations like this. So check if the lines are strait in Glyphs.

Thank you. I can see that they’re not straight in Glyphs, and I see how I can straighten them.
However, some straight lines are off as well. Is there a way to avoid deviations to begin with?

Probably the best to draw the outlines in Glyphs right away. Much more precise than Illustrator!

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There’s a tutorial about importing from Illustrator. It also explains grid and how to disable the grid, and its pros and cons.