A Hard drive camcoder with AV input?

Salam. I understand your requirement. Stick to MiniDV camera, I suggest Canon XL2. It has og AV in/out and firewire too. For projection to screen you use AV output. For saving into AVI files, connect firewire cable to computer. The operation can run simultanoeusly. If firewire cable length is not enough, you can use dv splitter to join within two firewire cables. One length is 20 meter. Canon has a big capacity battery for longer time of recording. So that you can record on to tape, project and save as AVI files in one time.