I guess I would just encourage you to remember that sometimes things have to get a bit messy for our kids to learn. The messes may not be as bad, or as numerous as you think! In fact, I much prefer cleaning up an occasional pee puddle than changing diapers regularly.
I'm all for the mama takes control, cold turkey method - not the relaxed, let them do it when they do it approach, which is a lot of the advice you are getting (diapers at 5? I feel badly for that child). And it has been a very positive and successful experience with my kids! Potty training is not a developmental hurdle that our kids cross on their own like learning to crawl or walk. We actually are responsible to TEACH them this one!! :-) Would we wait until they were 9 or 10 to have them start reading, because they just "didn't show much of an interest at 5"? Kids can be lazy about potty training, or just be afraid of making mistakes. They need us to show them that it's ok to make mistakes, and give them the confidence to try again and succeed. I trained my son (my oldest, now 4) at age 3. I was soooo nervous, he probably was capable sooner, but I kept putting it off for the same reasons you mentioned - accidents, he resisted, treats weren't enough motivation, etc. When I put him in underwear cold turkey, he got it so fast, and was SO proud of himself that I felt bad I hadn't given him the opportunity to do it sooner. And my daughter (2.5) was trained just a few months ago. And she probably could have also done it sooner, but timing was complicated with me being pregnant, then her baby brother arriving, then moving to a new house. So we finally tackled it Jan 1, a month after our move, and haven't looked back. She still has an occasional accident, usually right next to the toilet because she waited a bit too long.
Maybe to keep messes contained, play in one room with the door closed, the rug rolled up or a dropcloth out, and a potty chair in the corner for a day or two, while they adjust to wearing underwear. Then gradually venture out into the rest of the house as their success grows. You can set rules about sitting on furniture, or use waterproof mats on the couch if you feel better. Or keep them mainly in the kitchen or other hard floor areas. Reserve pullups for naps and nighttime only, take a foldable potty seat out with you for use in public restrooms, or some people even keep a spare potty chair in the car for use on the go. Just put a bag in it to catch the contents.
Don't let your fear of cleaning up a few messes hold your boys back from something that they really need to learn! They'll figure it out and be on to other things before you know it.