I see what the problem is, the gradients are defined differently in ai and pdf from inkscape, but I don't see an easy way to fix it!
You can manually move the four gradient stops (for any one of your objects) to the locations in the image below.

- g23287.png (24.38 KiB) Viewed 2104 times
If you are adept at text editing, you could then do some quick cutting and pasting in a text editor in the gradient defs section of your svg file to make the gradient stops for each gradient have the same numbers as your modified gradient.
Some one more fluent in xml might know of a substitution for "userspaceon use" in the gradientunits and "pad" in the spread in gradient defs that would have fix the output.
Your mind is what you think it is.