Yes, you can remove that tray. It gives a lot more room to get back there. You can also remove the battery/battery box/plug wires and get some good access from that side as well. You'll pretty much have to swap that connector out by feel.
Edit - For the tray, you remove the small grate and there are two screws holding the wiring harness box to the tray. Remove those and let the harness move around. There are then two or three small bolts holding the tray to the firewall at the top edges. Remove those and then you can pull the tray up while twisting it to get it out. There should also be a thin piece of plastic between the tray and firewall that covers the cabin filters, take that out with the tray.
CirrusSR22 has a great writeup of the whole cooling system rebuild. You might want to consider doing everything if that connector failed.
http://www.318ti.org/forum/showthread.php?t=18066 Driving in the red for even a couple minutes can weaken the headgasket/warp the head. You can rent compression/leak down testers to check the motor.