Since you say you're going to try to do the parks without an
ECV at first, I'd suggest really keeping track of how you're feeling and try to leave (or rent an ECV/wheelchair) *before* you start having real problems. Same with any pain medications; take normal ones on your normal schedule, but if you have breakthrough medication take it at the first sign that your pain might be higher than normal. It's far harder to recover after fatigue or pain is too high than it is if you preempt the serious problems. You'll also likely actually end up using less pain medication and need less rest if you're trying to stop before the problems start. If you think you just need a quick rest (rather than going back to where you're staying), it's possible to lie down at the First Aid centers in the parks. You can also call an offsite vendor after your trip starts if you decide you do need an ECV, but it might take them a day to deliver one to you. As well, my experience was that renting for a longer period often did result in a lower cost when averaged out over days than shorter rentals (usually it's at around a week that you'll definitely get a price break, but it depends on the vendor).
Honestly, with your description in your original post, I'd expect to be renting a wheelchair or ECV within an hour or two of first reaching the park. If you're trying to go all day, you'll be walking an absolutely minimum of 4 miles and probably more than 6. The majority of that walking will be between attractions so not something where most ride queues make much of a difference. There are no places to sit in queues (and no way for you to wait elsewhere and meet your party when they get close to the boarding area). Even when I first started having problems (I don't have a fibro diagnosis, but many symptoms of my diagnosis do overlap with fibro), I couldn't have done those distances multiple days in a row due to aches and fatigue even though a year prior I was competitively running cross-country for my high school.
With the amount of money a trip to WDW costs, you're better off finding the money together for renting an ECV or wheelchair from an offsite vendor than to overdo it early on and spend the rest of your trip in the hotel.
ECVs from an offsite vendor are far less expensive than renting in a park. Wheelchair rental is far less expensive than an ECV (offsite probably about $50 for a week), but you'll need someone to push you in it and WDW is not flat so it can be a lot of work. You could also push it when you feel like walking and sit when you need to sit (you still want someone with you who can push if needed). Either way, using the mobility aid could substantially improve what you can do in the parks so that you'll get more out of your park ticket.
With either a wheelchair or ECV you would have the option to only use it between areas and walk through queues, as well. That said, WDW mostly has mainstreamed queues so it isn't really much extra hassle to use the mobility aid in the queue compared to walking through the queue. There are also a couple very long queues in terms of distance (1/4 mile one way with no way to shorten that) so having that seat could be more useful in queues than you realize. Using the mobility aid will help conserve energy. Also, if you're at all touch sensitive, a mobility aid will provide a little more buffer from other people bumping up against you.