To clarify: I would run speaker wire from amp to monitors, then from monitors to sub (providing it has speaker level controls). Is this correct?
This is correct, though there are a few different ways to do it. The ownerÂ’s manual will give you a few scenarios, try them all and see which works best in your system. You can use cheap speaker wire to try different configurations. Go online and read a Def Tech sub (or other brands- like the ones blindjim suggested) owners manuals for examples.
Blindjims advice is good. Look for something that has the controls to integrate properly.
A word of advice- NOT HAVING A SUB is better than a sloppy cheap sub. You can pick up a used Def Tech Supercube 1 with speaker level inputs for under $600. Great sub, I have one in my second system.