S., I think the best thing would be to visit the fire department and/or the local police department and ask them for help with the car seats. They know all about the transportation laws and age limits, so they will be the best as to how to advise you to place the car seats, given the fact you own a pickup truck. I see kids (first graders and older) riding as passengers in pickup trucks, and the police don't blink an eye, but then again, this is Florida, and the laws on car seats and the ages of kids are very lax. Maybe Ohio is stricter. No, the laws are NOT the same in each state. They are determined by the state.
I have also seen kids riding on top of bicycle hand rails with their parent, and on scooters, either behind of or in front of their parent. They go to school like this on a daily basis, for years. If they can do it given their mode of transportation, so should you. Having a truck does not make you an unfit parent, or subject to lose the ability to foster kids. One of my daughter's friend's mother had a pickup truck with only the one bench seat at the front. She bought the truck when she relocated from Arizona to Miami and has never had an issue getting pulled over or deemed an unfit parent.
I realize that you bought this truck before the kids entered the picture and not everyone can afford to buy a new vehicle on a whim. Unfortunately, that is life. Some people cannot afford to get rid of their old cars that have no shock absorbers on the bumpers, for example. Still, that is not a reason to have the parent get in trouble. Having them in the driver's seat or in the pickup truck's bed, on the other hand, MAY be grounds for trouble. I could never foster a kid, much less 3, so I have no right to judge you and if anything, I congratulate you on giving these kids a new home and a new chance. It takes a special type of person to do this.