I have exactly the same problem with the d-roller. Ilford GGFS is very stiff, and it seems like the paper's leading edge leaves a "wave" in the paper when it wraps around by one full turn. On the second turn it either does not happen or is so slight that it's of no consequence. I've tried starting the print's leading edge further out instead of pushed toward the d-roller's core as far as possible. That seems to help a little, but it does not entirely eliminate the problem. It makes sense that all very stiff and fairly thick papers would have the same problem.
The d-roller has worked the best and fastest on mat papers, which are typically much more flexible than the Ilford GGFS. I've never seen a hint of a problem with these. I've also never seen a problem with RC papers (Epson Luster and Semi-gloss), though it takes far longer in the d-roller with these. I've not been able to eliminate the problem with Ilford GGFS. It makes sense that rolling the paper onto any other sort of core would have the same problem, and it would likely be worse because you would not have the rubber spacer between layers of the roll as you do with the d-roller.
I'm afraid this isn't any help, but misery loves company and you're not the only one with the problem. Short of flattening the paper in a dry mount press, or dry mounting the print, I see no solution. Note that Ilford does not recommend dry mounting due to the heat, so flattening the paper in a hot press is likely not a great idea either.