I'm mostly a DBA with some SA duties and I've been assured by our network people that having the two SIDs be the same on both domains is something that A: They don't want us to do, manually setting SIDs; B: You shouldn't do because the SID is a combination of User, Machine and Domain factors to create a unique key (not sure but this is what I was told) and C: If this works it is most assuredly a failure in the Microsoft Security that constitutes a major hole. As in, everyone run in panic scream and shout the world is ending... ( I suspect that's a bit of an overreaction but it's an accurate description of the reaction I got).

Bottom line I can't get access to the external domain to either get or set the SID for a user in that domain. If I can't be allowed to know what it is I can't set mine, and I certainly can't set there SIDs.

I'm going to try and find a suitable Microsoft OS and/or SharePoint forum to post this issue in and I'll write back here with a resolution if I can get one.