If the inside ski is not being released, you're going to have to lift it when you want to make turns quickly in situations where you can't pivot them effectively (e.g. powder, bumps, low speeds). Pulling the new inside foot back and smearing can be used as a stepping stone to get the new inside ski to flatten and then go onto the new edge, but (as you've seen) those moves alone don't solve the whole problem. Part of the problem here is that we need to be talking about two different types of turns: crossover and cross-under. One place where you have to be using cross-under turns is when your upper body flows straight down the fall line. Here your skis have to be turning underneath the body (or else you'll be doing a straight run). When your upper body has some lateral movement across the fall line its path typically shortcuts the path of the skis to create crossover.
You can make short radius turns with crossover movement. Ideally, you will finish the old turn with your shoulders and hips faced to the inside of what will be the new turn and let your upper body flow across the skis in that direction to initiate the new turn. This movement will pull the new inside ski onto the downhill edge and cause it start turning in the new direction. That will eliminate the need to lift it to get it out of the way of the new outside ski. If you finish your old turn with your new inside leg too far forward (and thus your hips and shoulders are facing more in the direction that the skis are pointing vs the inside of the next turn) it ends up blocking the path where your upper body need to flow to get to the inside of the next turn. Pulling that foot back can create room for the body to flow, but smearing the turn moves the upper body behind the feet instead of inside of them. The next step is to introduce movements that let the body flow to the inside instead. One key movement is bending the new inside leg (make it shorter) and tipping it into the new turn. Before I get to that step though I usually work on the previous turn finish so that we don't let that to be new inside foot get so far ahead that it needs to be pulled back.
The second problem is that in powder and bumps when we want to make short radius turns we like to flow straight down the fall line using retraction turns where the skis cross under the body. Here we have the same bending and tipping movements of the legs as the cross over moves, but they are amplified because we don't have the "help" of the upper body flowing across the skis. Instead we have more of a sensation of sucking the legs up underneath the body from one side and then pushing them out to the other side. Depending on your point of view this could either be seen as the ultimate in pulling the inside foot back and smearing or a total antithesis of these concepts. If you're really good, you could smear or carve your short radius turns to support either viewpoint depending on your control of edge angles.
Here's a drill for you that should throw some light on the subject. Start by traversing across a trail stepping from foot to foot. Try quick low steps and long high steps. Make sure that when you step the lifted ski either stays level to the snow or is slightly tail high/tip low. Next try traversing across a trail picking up the uphill ski and tapping the tip of the ski on the snow. It helps to pick up your knee to pick the ski up and push down with your toes to tap the tip down. When you can do this in both directions, try the downhill ski. When you can do that in both directions try initiating a turn with the downhill lifted tail of the snow, tip pressed into the snow and tipped into the direction of the new turn. When you do this you should feel your upper body being pulled into the new turn. When you've got that on easy terrain and snow, take the move into problem terrain and snow. When those turns start to feel good, "quiet" the movements until the inside ski no longer comes off the ground. Then you'll be skiing without lifting the inside off the snow.