It helps to understand how ratties think.
They can't see very well, so they rely on scent. They are territorial, so they have to mark things to know what's theirs. They also are inherently neat. They don't like fouling up their personal places with feces so much.
Rat poo and urine is easily the least noxious of all the rodents I've dealt with--mice, gerbils, hamsters, guinea pigs, or rabbits.
I would have said this is a universal truth, but I do have two newly aquired slobby naked rats who are the exception to that rule, and who unfortunately have pretty pungent poos--they smell like little tiny horse manure nuggets.
I found that in my bathroom, my rats would only pick two places to drop raisins; their chosen personal potty spots-- Under the vanity desk (a spot out of the way and under cover), and in the bathroom closet (again, out of the way and under cover). So, I put a carpet square in both areas and set up a litter box for those spots. Adult rats are better at this. Much like puppies, young rats need to learn.
Rats tend to mark things they 'own' with little dribbles of urine. Full out peeing they tended to do only in their litter box, though every rat is a little different. Again though, rat urine is remarkably non-noxious stuff.
I noticed that in the bathroom, that the areas they would mildly mark tended to be their favorite hang out spots, or their favorite running paths along the baseboards. They don't usually pee or poo a lot or indiscriminately except when they are fearful or overly excited. My mice on the other hand? They would pee and poo every flippin' where, and it REEKED.
My rats will dribble a little piddle on me too since they luv me, but I've got a 'rat hoodie' that I wear only when interacting with them. I don't wash it, so it always smells like them, and even if they mark it, it's not a big deal.
So no, you can't get them to quit completely, but they are predictable and manageable with a little forethought and creativity. Do figure out a way to let them have their hour a day out. It will make them much happier and calmer, and much more friendly towards you.
Are they male or female? If they're females, they probably always be more hyper. That's one of the differences between males and females. Females love to run, jump, and play. Males are lazy lard butts.
An idea, if it's in your budget, or if you are crafty and can cheaply create something on your own, is to use a ratty playpen on top of a double ply blanket. A friend of mine got the Martin's playpen which is between 61-74 dollars new. She lays out a blanket on her bed, and puts the playpen on top of the blanket. It works great! It contains them and gives them plenty of running space. It also has a lid to prevent climbers from escaping. You can build your own though with hardware cloth.