"Control" means securely, with solid belays, and with an attention to detail, as well as not falling off.
Moving well, or fast, on ice melts down to two basic components: The mechanical systems (most of the last post on multi-pitch ice) and then the physical stuff including technical ability, your partner, etc. This post has to be a bit brief 'cause I'm blowing off some other stuff to write this, but I've been thinking a lot about this in the last few months, so here are a few more things. Note that they also generally apply to single pitch routes. There's just not much technical difference between climbing single and multi-pitch routes well, it's the mechanical transfers that are different. My book goes into this all a lot more, but here are some recent thoughts:
1. Look at the route from the ground for at least five or ten minutes. Line selection is everything on long routes; if you want the "hero" line then you can find that, but most of the time on long routes you just want to get up the rigs as safely, smoothly and enjoyably as possible. It can be really hard to pick lines while on the route, especially on bigger and steeper rigs. A bit of short-term effort can bring a climber to a long groove of good ice that's not obvious while on the route... Stop, look. I often watch people struggle for literally hours on routes that would be a lot easier if they would just move over 30 feet or something. This study will also lead to good belay stances. Talk about this all with your partner; a team understanding just seems to help, and keep things running smoother.
2. The same thing applies on a small scale. Ice is often radically different just a few feet to one side or the other. All the stuff about where to swing (in concave places, not convex) holds true. Good ice tends to form in lines; inside of corners, the thinner ice on the edge next to the rock (usually better than the fat stuff if the ice is only 3M or so wide...), etc. etc. You can take twice as long just by climbing one meter in the wrong direction.
3. If you do the above right you'll probably move generally OK.
4. How often to put in ice screws? As often as you need to, but always have enough solid gear in to keep you from either hitting the ground or a ledge feature that will operate as the ground. If I feel strong and secure I'll run it hard on steep terrain. But if gets ledgy and messy I'll always put in a screw just before pulling over a bulge above a ledge... It's all about the situation you find yourself in, or rather, knowingly climbed into 'cause you were reading the route above you and had an idea for the line developed on the approach. I have seen way too many horrible broken ankles, legs and other carnage from people falling off on ice, even while being lowered on ice and dropping a few feet onto a ledge. Crampons and falling just do not mix; sometimes you'll have good luck and it will all be OK, but personally I try to climb like any fall will result in a compound fracture of both legs. It's worked for 25 years.
5. If you can't lead most any ice pitch you encounter in under about 30 minutes and any ice pitch you encounter in under an hour then you're climbing over your head and shouldn't be there. Go back and learn how to climb better, or choose an easier line. I mean this. Alpine pitches are a bit different, but most pure ice pitches should take under half an hour to lead. If they're taking more than this you're either trying to climb up to the level of your ego (the pitch is too hard even if you think you should be able to do it), you're trying to impress someone else (same), or you've screwed up and are trying to get it done (it happens, I was there a month ago). Realize that you're pushing things, your partner is going to get cold and not be having any fun, and that you don't have a safety margin anymore. Ice climbing is fundamentally not about technical ability but balancing ability and ambition; I'm a lot more impressed with someone who can lead a "grade 4" smoothly and well than some joker who sketches up a "grade 6, dude!" then boasts about it in the bar. If I sound a bit sarcastic and maybe a little aggro here it's because I've seen far too many leaders on terrain far too hard for them over the years. I've left climbing areas rather than watch someone sketch their way up something. Compound fractures are messy, I don't want to watch.
6. Strength will help in ice climbing for sure, and all things being equal the stronger climber will kick ass on the weaker climber. But all things aren't equal. Most ice climbers need to train on ice way more than they do. Do 200 laps on a vertical ice climb and you'll likely have a clue about how to actually ice climb. Do 20 leads on vertical ice and you might not know much about ice climbing. There is a replicable, teachable, and organized method to climbing ice well; learn it well before you lead. Nobody would grab a rack of cams and head up a crack without ever actually having climbed a crack, yet that's what I see all the time on ice climbs from rock climbers. The idea is to move securely, smoothly, and at a speed that can be maintained with those two attributes...
7. Have fun. If you're not having fun and enjoying the place, the day and the setting then you're probably climbing too hard, and climbing fast is out of the question. I know I'm "on" when I'm psyched, moving securely, feel strong, and it's all working. I know it's off when I keep thinking about how I'm going to get some work done at the office or something, I feel cold, I'm climbing slow and awkwardly, etc. etc.
8. Bring a couple of little "family band" radios on long routes. These really, really cut down on confusion on ice climbs. I've seldom needed them on rock, but they are great on ice and cut down on yelling.
9. If the leader takes 30 minutes then the second should take under 15 from the time the leader yells "Off!" to when the second arrives at the belay. Enough said.
10. Train. This is the secret to climbing ice. In order of usefulness: Train on ice, drytool, train on plice, train in the gym (straight Crossfit will be enough), train however you can come up with but train.
OK, there's a rant, lots more to put down but I'm out of time. Have fun!