I really wouldn't worry about how many oz of milk she is having, as long as you offer her milk frequently and let her take as much as she wants. The main thing is not to enocourage her to cut back or drop feeds too quickly, but you can't force her to drink it, as you well know!
As MrsBadger said, if you were breastfeeding you'd have no idea how much she is having.
This is the official Dept of Health weaning guidelines that you and your HV should be following - notice there's nothing about minimum amounts of milk and it says to offer your baby finger food as soon as they are interested.
Some babies are interested at 6 months, some take a bit longer, but it will do no harm by iffering her some finger food from the word go. If she's not interested that's fine, but if you don't offer it you won't know.
WRT choking, the main things to remember is to ensure she is fully upright when she is eating, not reclined, and let her be in control of the finger foods that she puts in her mouth, ie don't break off lumps of food and pop them in for her. Generally baibes won't try to eat finger foods until they are developmentally ready to eat it, though to begin with she will spit most of it back out again. That's fine too, it's all part of the learning process.
And to repeat MrsBadger [again } don't confuse gagging with choking. Gagging is when a piece of food moves too far back in the mouth and triggers the gag reflex. usually the baby will cough and splutter a bit, the offending piece of food will move forward and baby will carry on quite unperturbed - much more of a parent frightener than anything else. Choking is when food gets lodged in the windpipe. More serious but much much rarer, especially if you follow the guidelines I previously mentioned.
Google Baby Led Weaning. You may not want to follow the whole philosophy (I did with DS2 and it was fantastic, I'd never wean a baby on purees again, but that's just my view) but it's still very good for safe finger food ideas.
Just keep everything relaxed and happy, offer her a good range of foods and plenty of milk and I'm certain she'll do just fine