We would like to be able to search for issues within a subset of projects.

I can think of two ways of implementing this:
(1) Add the ability to search all but exclude certain projects, or to include only particular projects
(2) Group projects, and allow searching within groups of projects.

I realize you'd loose custom fields when looking across projects where some have the fields and some don't, but it's more important for us to be able to look for all issues in several projects. (maybe the custom fields that are common across selected projects could be displayed?)