” the camera is already pretty small (about 3 pounds with the Rode) and the tripod is rated to hold up to 16.5 pounds.”
That’s very light – no wonder you have problems. My camera alone weighs more than your camera and tripod, combined. I think a heavier-duty tripod and pan head could be beneficial, for the inertial damping. It’s also not clear to me that you have an actual fluid-head pan head, or just a spring-tension/friction head – that’s kind of important.
As to checking the balance on the rig, it’s not complicated: you loosen the locks and let go and see if it wants to tip up or down. There should be an adjustment on the camera plate/pan head interface for positioning forward and back. In some systems, this is a knob that, when loosened, allows the entire assembly to slide a bit forwards or backwards on the plate, until everything balances. Less-sophisticated/cheaper systems offer a row of screw mounting holes on the underside of the plate, where the “wedge” attaches to the quick-release on the pan head. You can do a gross adjustment there, by picking the next screw hole forwards or backwards and re-locating the wedge. If you can get close to perfect balance, you can theoretically let the thing go and it will stay put, even with the locks off. That’s the ideal. You might need to add a heavier battery pack on the back, or attach a little bean-bag or lead weight of some kind under the front, to get to “perfect”. In some cases, one might get a piece of sheet metal from a home center, drill the appropriate screw holes in it, and sandwich that in-between the wedge and the plate, to both add some mass, and a place to attach accessories.
You can get a 4K go-pro knockoff these days for between $45 and $70. Once you get this for your b-roll and wide shot covers, you’ll wonder how you ever got along without it.