If you are "trusted" enough on one site, I don't see a problem with copying the profile over (ie, if this is a bug report, it's one that probably would be "no fix").
If you are highly trusted on the original site, you'll get enough of a bonus to edit your profile with links intact (as Aether points out).
If you merely want to work around the limitation (which is a corner case and probably won't be fixed, even if it's determined to be unintended) then you can edit the profile fully on the original site, then copy it over again, then revert the original profile back. This will allow you to have all the links you want with separate profiles on both sites.
Of course, the real solution is to gain rep on the secondary site so you gain those privileges naturally...