Believe me, I understand. Unfortunately there is a lot of casual ableism on these boards sometimes. Mostly unintentional, because I absolutely believe that people generally mean well, but sometimes there is an air of "if you can't do things exactly like an abled person could then don't bother to go" and a lack of understanding about invisible disabilities as well. We just have to do a little more planning than most, and it means listening to our bodies and being flexible enough to drop a planned activity if we are feeling overwhelmed.
If you are open to moving your dates, early May is great, the weather is nice and crowd levels are still fairly low because spring break is over but school is not quite out yet. I find routine is very important to keep stress levels down. I still practice the same mindfulness exercises that I do at home. Your plan to go slower and over a longer period is a solid one I think. 10 days sounds like a long time but our upcoming trip is 11 and we only plan on rope dropping a couple of days, taking advantage of afternoon LL stacking and Extended Evening Hours since we will be at the Poly is going to be our strategy. Crowds are a big anxiety trigger for my partner but she has a great time because we take it easy and know how to avoid them. In the past that meant things like dessert parties for the fireworks. I agree with PPs that if you can afford to do so a VIP tour sounds like it would be a great fit for your family, and booking one would give you access to DSS assistance. I would explain the situation to them at the time of booking. I would also strongly recommend you skip rope dropping entirely, those crowds are insane now.
Quieter areas in the parks are important for breaks even during minimal park time. If push comes to shove, don't be afraid to go to First Aid. They have quiet, dimly lit spaces to sit if you need them and I have used them when overdoing it in the past, the nurses are always very accommodating. Disney actually publishes a guide to quieter areas in the parks though, it can be downloaded here:
https://disneyworld.disney.go.com/guest-services/cognitive-disabilities-services/
There is also a guide to attractions on that page, explaining what kind of stimuli are involved in different ones (such as loud noises, sudden drops, etc) though it's a bit outdated.
You mentioned your kids and World Showcase, I would strongly advise to avoid it Fri-Sun as the locals are out in force during festivals (which is like all the time now) and this is peak "Drunkcot" time with crowds and rowdy guests. Linger after the nighttime shows to let the crowds thin out before leaving. In general keeping a slower pace and zigging while others are zagging is key. Also agree to make sure your needs are being met as well.