You can disable BBEdit from opening a new document when you start the app, so that would eliminate the cursor on the new document--Preferences, Application, "When BBEdit becomes Active" → Do Nothing.
However, the search field still blinks.
You can wrap the search in an Automator Service which will just open the results when completed so you don't have to interact with the search input box. But, I imagine the result window will still scroll.
If you think this will help,
Create a new Service in Automator.
Have it receive selected files or folders in Finder (or PDF Files -- likely better since that is the only valid file type).
Drag in a "Run Applescript" action from the Utilities Library.
Change the script to this:
on run {input, parameters}
tell application "BBEdit"
find "JPXDecode" searching in (items of input) with showing results without text files only
end tell
end run
Save the service with a useful name like, "Find JPX PDFs"
In the Finder, right-click (or ctrl-click) on a folder with your PDFs and choose your service from the Services menu.
If you use PDF files for the "Service receives" target, you could just select a short list of files to check to prevent the search results from scrolling.
I would imagine other text editors might offer multi-file search. If you have one that works for you, maybe try using it to search for that term.
Also, I would think this might be possible using the Terminal. Maybe one of the Unix gurus could offer another solution using the Terminal.