A., bless your heart. I totally know what you are going through. I have 3 as well and when the third was born my others were 1 and 2 yrs. They are now 5,4 &2 and I hate to tell you that I am not in any better shape now than I was then. However, I have somehow learned to function on basically no sleep.
You are correct, putting them to sleep later isn't the solution for us either. I have quit fighting the nap thing because they won't sleep at night if I am even able to get them to nap (rarity). Lately, I have started putting them to bed at 6:30 instead of the usual 7:30 (easier this time of year) and even if they don't go to sleep immediately, it allows for some rest time. Also, i insist on 1-2 hours of "quiet time" in the middle of the day. THey are allowed to hang out in their rooms or sit quietly watching a video or coloring. It really requires a lot of supervision on my part because they tend to get ramped up and start running again. I have to take the time to make them remain in "quiet time".
This helps with the afternoons a lot! However, it hasn't done a thing for the sleeping at night. Since afternoons are crazy, I bathe them and feed them around 4 or 5:00 - weird, I know, but if they crash and burn, they are ready to be put down. THey can always have a healthy snack later if they make it.
Fans in their rooms will help keep them from hearing what happens in the morning and might help them sleep a little longer, but it is no guarantee.
As odd as it sounds, mine tend to sleep later in the morning if they have gone to bed earlier at night. If they actually go to sleep at 6:30 PM, they'll sometimes sleep until 7:30 or 8:00. Go figure?????
Bear with it - go to bed when they do if you can. Try to remember that they are only little once and you'll miss it - (I have to remind myself constantly AND I also have to go watch them sleep at night to remind me how much I love them).