Dale, if you are heading for the surface every time you fin at depth, you don't need ankle weights or heavy fins or to push your tank down lower or even a different set of dive instructors. You just need to think a little about the physics of it.
If you fin and you head to the surface every time, chances are that you are angled with your legs lower than your head and shoulders so that the force of your finning sends you upwards rather than only forwards. This is essentially a problem of trim, and most often caused by improper weighting. When you've got too much weight on your belt, in your pockets, etc., you need to put extra air in your BC at depth to compensate for the weight (in order to get neutrally buoyant). The air in the BC lifts your upper body while at the same time all the weight you are carrying is dragging your hips down. So you end up at some angle rather than parallel to the surface of the water. We want to be parallel to the surface so that our fin kicks will push us forward.
At the end of the day, the diver him/herself is the only one who can make adjustments in trim. Instructors or buddies can tell you whether or not you're in trim, take a picture of you to show you or even grab you and put you in position, but really, you are the only one who can keep yourself in position. Getting your weighting right is the main key, and linked to that is getting the weight in the right place.
For people who need to carry a lot of weight because of thick wetsuits, body type or whatever, a stainless steel backplate, or putting some of the weight in trim pockets or on the tank strap can help shift the weight off the hips. I suspect that your instructor's suggestion of a BC with integrated weight pockets is an attempt to get some of the weight off your hips and higher onto your rig. I sometimes actually attach weights onto my students' shoulder straps to achieve the correct balance.