Would it be possible to power the Raspberry Pi from the same 5V supply as the IO Pis and the relais boards?
The problem could be that if the Raspberry Pi is already powered when the IO Pi is unpowered then the I2C level converter will still be supplying about 2.6V to the I2C pins on the IO Pi chips. This could be causing the IO chips to pull the output pins high while the chip initialises. If you use the same supply for the Raspberry Pi and the IO chip or can make sure the two seperate supplies switch on at the same time this should solve the problem.
There are a couple ways you could connect the power supply up to the IO Pis and the Raspberry Pi, you could use seperate cables to connect to the IO Pi boards and the Raspberry Pi while leaving the jumpers disconnected, this would mean that while they all receive the same power you wouldn't have the problem of the power back feeding into the Raspberry Pi from the IO Pi.
Alternativly you could connect the power to the two IO Pi boards and leave one of the jumpers connected so the Raspberry Pi is powered through the 5V pin on the GPIO port. The downside of this approach is it would be bypassing the input protection fuse on the Raspberry Pi so if you accidentally shorted one of the GPIO pins to ground you could damage the Raspberry Pi.