Here's an example of the command to use:
find . /Volumes/My\ Book\ for\ Mac/ -name '*.txt' -atime +1 -ls -exec grep alato {} ';' > my-book-for-mac-escalator-search-take1.out
This command searches all *.txt files on the disk for alato. (I'm looking for all files that contain the word escalator, but am using "alato" to make the search go faster. The search string "alato" is just long enough to keep the number of false hits down to a reasonably small number. I'm not sure how much time you save with this trick, though. And it's too time-consuming to test it. [Note that you also have to keep in mind that recently read files are cached, which speeds up the next search considerably, thereby thwarting your test.])
I tested this "-atime +1" trick and it works!
One of the files in the output has an inode number of 11570349. If I search for that with the command that uses "atime +1" I see it only once. If I search for it with a command like the one above, but without "atime +1" I get 115 hits. Unfortunately, the one with "atime +1" took 11h42m, while the one without took 13h01m. So the overhead per hard link is significant. OTOH, you get an output file without multiple hits in it.
With "atime +1":
find . /Volumes/My\ Book\ for\ Mac/ -name '*.txt' -atime +1 -ls -exec grep alato {} ';' > my-book-for-mac-escalator-search-take1.out
new-host:ESCALATOR SEARCH root# grep 11570349 my_book_for_mac_escalator_search_take1.out | wc -l
1
Without "atime +1":
find . /Volumes/My\ Book\ for\ Mac/ -name '*.txt' -ls -exec grep alato {} ';' > my-book-for-mac-escalator-search-noatime.out
new-host:ESCALATOR SEARCH root# grep 11570349 my_book_for_mac_escalator_search_noatime.out | wc -l
115
The file sizes:
-rw-r--r-- 1 root staff 144463769 Jul 26 01:45 my_book_for_mac_escalator_search_noatime.out
-rw-r--r-- 1 root staff 3455675 Jul 24 08:24 my_book_for_mac_escalator_search_take1.out
If there's a way to search by inode you'd be guaranteed to search each file only once. But then you have to find a hard link that goes with that inode. I don't know if that would help much.