I have just finished hand-weeding an 800 sq ft garden. The weeds were
everywhere and, because I didn't get all the weeds and/or their roots,
I'm sure that, in the very near future, the weeds will re-sprout.

What can I use to kill the remaining weeds and/or their roots without
harming the established shrubs in the garden? How do I apply that
product?

(I want to kill the weeds BEFORE I blend a 2" layer of redwood bark,
kelp meal, worm castings, bat guano and chicken manure, etc into the
top 6" of soil) and plant new shrubs.