Wolf's responses are right on the money. Since your amps have volume controls on their inputs, you can turn them down to zero and then safely disconnect and connect i/c cables. This will leave the power amps powered up continuously and avoid stressing them through repeated off/on cycles. It also means that you avoid any changes in sound due to the power amps being turned on and off.
As far as the preamps are concerned, you can certainly leave them all powered up so each one is ready to go when you want to change from one to the other. This will leave each one in a good-to-go status without worrying about changes during warmup. You will be switching the input connections for each preamp as well as the outputs, so that only one preamp is actually connected to the source at a time. The idea of running all 3 preamps in parallel and using a switching box between the preamps and the power amps makes no sense at all. You not only have the sonic colorations of the switch itself but also the unnecessary i/c cables. It is far better to take advantage of the amps' volume controls and then move all of the input and output connections from one preamp to the next.
Two final comments. First, leaving the unused 3 preamps powered up while you are listening will change the sound compared to just having the one being tested powered up. There is nothing wrong with leaving all 3 on for some initial comparisons, but eventually you need to listen while just one is powered up. The true sound of the preamp will only be demonstrated when the others are turned off and the power cords unplugged from the outlets.
Second, the point about needing to do longterm listening is valid. There are aspects of the sound that become apparent only through longer listening. Sometimes differences are masked when you change quickly from one component to another. That doesn't mean that you shouldn't ever change quickly from one to another, only that you shouldn't use this as the sole means for evaluating components.
As far as the preamps are concerned, you can certainly leave them all powered up so each one is ready to go when you want to change from one to the other. This will leave each one in a good-to-go status without worrying about changes during warmup. You will be switching the input connections for each preamp as well as the outputs, so that only one preamp is actually connected to the source at a time. The idea of running all 3 preamps in parallel and using a switching box between the preamps and the power amps makes no sense at all. You not only have the sonic colorations of the switch itself but also the unnecessary i/c cables. It is far better to take advantage of the amps' volume controls and then move all of the input and output connections from one preamp to the next.
Two final comments. First, leaving the unused 3 preamps powered up while you are listening will change the sound compared to just having the one being tested powered up. There is nothing wrong with leaving all 3 on for some initial comparisons, but eventually you need to listen while just one is powered up. The true sound of the preamp will only be demonstrated when the others are turned off and the power cords unplugged from the outlets.
Second, the point about needing to do longterm listening is valid. There are aspects of the sound that become apparent only through longer listening. Sometimes differences are masked when you change quickly from one component to another. That doesn't mean that you shouldn't ever change quickly from one to another, only that you shouldn't use this as the sole means for evaluating components.