I don't remember if you kept your character breakfasts or not, but if you did I do think driving to the parks on those days is good as you won't have to worry about waiting for a bus and missing your ADR.
I agree about the deluxe dining plan, I think you will be happy you changed it. Last time we went we wanted to eat like we wanted (which would have required the deluxe dining plan) but pay out of pocket as we thought it would be cheaper. And it was. After paying tips the deluxe dining plan would have cost us around $2400 for 9 days (I think it was 9) or our family of 4. We paid out of pocket but still did 2 TS meals almost every day and "only" paid $1600 for food, a savings of $800. $1600 is a lot to spend on one week for food but hey, it's vacation and it was something we budgeted for ahead of time. In the end though, we thought 2 TS meals was too much for our kids who were 3.5 and 16 months at the time. When we go this April most days we only have 1 TS meal planned. The days we have 2 are for restaurants that are on the faster side or just ones we didn't want to miss.
As far as going back for naps, I say be flexible on that as we found it more difficult to go back for naps! But since you are going in June and it will be hotter and busier, you may not get much done in the afternoons anyway. But for us we couldn't get out of the park before the 16 month old was asleep, so leaving was pointless and the 3.5 year old was no longer napping and a nice long walk in the stroller was all he needed to regain his energy. We stayed out late a lot of nights too!
Hope you have a great vacation!