I did 8 hours on one side, not 24. Sorry the way I said it was misleading. When I swapped it was just about as difficult as usual since I had such an oversupply at that point that I was pretty much always busting. It helped to start the 8 hours in the morning so that when I switched it was evening when my supply is generally lowest. I hand expressed a bit more right before I switched, let her suck until letdown (about 1 suck) then took her off and caught the spray in a towel. Once the initial letdown slowed a bit I put her back on. That is how I still do it first thing in the morning when my supply is highest. Also, that whole day I dedicated to just nursing. We laid in bed so I could do laid back nursing and I even had snacks set up so that we didn't have to focus on anything else. The next day I stayed on one side until it felt close to empty then switched based on the cues of my body. I saw a slight difference that first day then an evening out a week or so later. Now, I really just listen to her cues and my body to decide when to nurse and when to switch sides. We do not follow a schedule. She still almost always nurses on only one side at a time and it usually takes her about 5 minutes. I still have oversupply and if she decides to sleep for a little longer than usual I feel really full and the letdown can be pretty strong. She still sometimes gags and yells at me, but mostly she has learned to manage what my supply is now. I have squirted a random passerby when she pops off with the initial letdown, but I try to be glad that at least I know I have enough milk for her. I never hand express now because I think it increases my supply. I pump while at work, but no other time and I make sure to only pump the amount she would have likely eaten. If I'm overfull I put her to the breast to see if she is hungry if not she just closes her mouth to it, but it is enough to start the milk flowing enough to be more comfortable. I just catch it in a towel (prob should catch it in a bottle).
Another thing that I find useful when I'm overfull is holding her in a way that is the same direction as my body. Whether sitting up, laying down or slightly reclined I have her feet toward my feet and her head to my head. Somehow this seems to help her to choke less. Also, she has reflux and as much as I didn't want to give her meds they have helped tremendously. It is worth looking into if you haven't. Not sure if you said you did or not.
Good luck with everything. I remember people saying to me "Well at least you have enough milk." and I always thought yeah well what good will that do if she can't eat it because it blasts her across the room or hurts her belly. Anyway, hang in there and I hope it gets better soon.