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http://www.forgeworld.co.uk/New_Stuff/FULGRIM_PRIMARCH_OF_THE_EMPEROR'S_CHILDREN.html

http://www.forgeworld.co.uk/downloads/product/pdf/fulgriminst.pdf

How do I build this model so I can remove the smaller base?

This model has 3 base parts, which are 1, 2, and 3 in the pdf.

I get that 1 & 2 go together, but any way I dry fit them, I can't remove 3, without the dead marine arms from 2 getting in the way.

What am I doing wrong?

I don't think you're doing it wrong... it's quite clear from the .pdf that part 2's arms go over the edge. It just looks like you're not meant to be able to remove it (which is a shame).
Seeing as it's only part of the scenic detail, you're not exactly mutilating the model by converting that rogue arm, maybe snip it down and green-stuff some blood or cables coming out of it?

Maybe shave part 2 down a bit so you can tilt and slide Fulgrim out from under it?

It's hard to say without all the pieces in hand.

Thanks, yeah that was the best I could come up with.

It is strange Angron just slides out and I figure Fulgrim would be the same. But, yep those arms lock Fulgrims base down, so off they go!