yes I too would try everything I could to recover, and honestly its sort of your job to do so
wanton waste is in most rule books and requires a hunter to make all efforts possible to recover a shot deer!
worst that can happen IMO< is land owners say no!
if you DO find it, or SEE it dead some place where they say NO< you can also TRY and get your local game warden involved, , some times them asking JUST for recovery will be granted over JUST you as a hunter, NOT always, but , again, all they can say is no
so would be worth it to me to try all things possible!