I find Tinderbox’s built-in search leaves a lot to be desired, but you can improve things by using an agent.
This TBX file (57.8 KB) has a top-level agent that will search for notes that contain all of the words in its $Name. (Note that unlike in the built-in search, the words can appear in any order and need not be next to one another, or even in the same attribute.) You can specify which attributes the agent searches by setting the agent’s SearchAttributes key attribute. This search is potentially quite costly, since it will be common to search through the $Text of notes, so if the agent has no words in its name, it deactivates itself, and reactivates itself when a word is entered into its name.
I usually have one of these at the root level of my documents ready to go if the built-in search doesn’t get the job done.
This still doesn’t do what you’re really looking for, in terms of searching every attribute. But it’s easy to add a large set of attributes to search, which is not possible in the built-in search.