Offset, centre bore and PCD are compatible between both models.
The GD alloy has a 185/55r15 tyre so the rolling circumference is 1836mm
The GE has either 175/65r15 or 185/55r16, so 1912mm or 1916mm respectively so as you state you would require a different tyre to the GE.
I think the 16" GE wheel would require an even lower profile tyre and hence poor ride so the 15" is the only reasonable option.
The 5.5J rim is 12mm narrower than the 6J but most 185/55r15 tyres are rated for widths from 5.5J to 7J, although a 175/60r15 tyre may be more suitable as it's recommended for 5 to 6.5J widths even considering it's larger rolling circumference of 1857mm (+1% over OEM).
The steel GD 14" and GE 15" alloy are both 5.5J ET55, so will sit in the arch the same.
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TG
GD 175/65 R14 ET55 5.5J 56.1 4x100 1832mm
GD 185/55 R15 ET51 6J 56.1 4x100 1836mm
GE 175/65 R15 ET55 5.5J 56.1 4x100 1912mm
GE 185/55 R16 ET51 6J 56.1 4x100 1916mm