Sleep is a habit, and you are right, you have conditioned her to eat at certain times. So, two things that work without relying on a full CIO:
1. Start reducing nursing time at each feeding, working on one wake up time at a time. When she wakes, nurse her, but keep track of how long you nurse. Gradually reduce it, reducing it by 30-60 seconds every 3 nights. When you are down to two minutes, don't run when she wakes, give her 5 full minutes. If she still wakes up, you can try my second suggestion, but there will be a few nights of 2-5 minute fussing before she just sleeps through her habitual wake up time, so you a have to give her time.
2. The 5 minute startle: this doesn't always work, but it does work sometimes. 5 minutes before usual wake up time, go into the room and make some noise, startle her enough that she rolls over. This will reset her sleep cycle and she should sleep till the next wake-up time.
It is perfectly normal for an 8 month old to need a night feeding. In fact, I think most babies need food till closer to 12-13 months, but they should only be waking once or twice, after a good solid 9 hours of sleep.
Also, it sounds to me like you really need to work on getting her naps consolidated. SHe sounds over tired to me. Use the 5 minute startle to get her to really nap. Anything less than 60 minutes is NOT a nap. So, you need to get her naps consolidated, and that will help her night sleep.
My son has a dairy allergy. I can eat whatever I want, but he can't breath and breaks out in terrible hives if he does near diary himself. It has NOTHING to do with his sleep. The fussiness your daughter is exhibiting is most likely a direct result of her being over-tired. Most 8 month olds can't skip naps. You may need to rethink your work-out schedule.
One last thing, pick feeding times and stick to them. So if she wakes at 9, don't feed her! Go in, and tell her it's "night night time, go back to sleep." If you don't have a sleep cue phrase, get one and start saying it every time you put her to sleep. Eventually, she will respond to the phrase and you can just say it from the doorway.
Two books: No Cry Sleep Solution and Healthy Sleep Habits. Both have lot of really good information in them.