Start relay smoking after AAW install.

This happens only during cranking, correct?

A few questions/ideas:
What type of starter is it, and how old?
Is there paint or corrosion on/under the ground cable's connection to the block/head (not sure which engine you've got)?
Have you checked your negative battery (ground) cable for internal resistance with a multimeter? I've seen new-looking ones that were solid green under the insulation.

My first impression is that it's ground-related, meaning you've got a weak connection there somewhere. To push through the ground problem it's dragging a ton of amperage through the positive side of the relay.