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You don't have to pull them out - just take the flange bolts out of the head on the driver-side header and move it up and tie it up out of the way. You need to have enough room to put your arm in to the top of the bell housing and loosing the bleed plug. Heck, if your arm is skinny enough, try and reach up there before removing the header.
Below is a shot of the torque tube and drive shaft out of the car. That's the slave cylinder exposed. That long black plug is what you need to loosen to bleed the system.
Yes, every C5 came from the factory with the tunnel plate. Vendors like Elite Engineering sell upgraded versions. You need that plate to stiffen up the chassis by tying the two main frame sections together and to reject some of the exhaust system heat.
Check to make you you have one and call Elite for one of their upgrades if it's missing.