I think your requirements need

a little refining...

1) What is the hot shoe going to be used for?

2) There is nothing under $2,000 with XLR audio inputs. If we stay with a 1/8" stereo audio input and augment that with an XLR adapter (juicedLink, BeachTek or separate audio recording system), is that OK?. Also, in the top requirements list, "Microphone Input (XLR/Standard Input)". But in the bottom you indicate XLR inputs are preferred but not required. What is "Standard Input" mean relative to audio inputs?

3) Most camcorders that capture video to flash memory cards do not have firewire. It is not necessary. Can you explain why firewire is a requirement?

4) I am not aware of any new "camcorder" under $2,000 that has a LANC port.

From the "preferred but not required" list:
5) Dual battery inputs? If cables are being run for LANC, is it OK to run a power cable, too? Or a battery plate that plugs into the camcorder's DC-input? Or do you mean that the camera needs to have two battery wells for internal batteries? I've not heard of that.

6) Internal memory? One of the requirements was SD memory. What would the internal memory be used for? Generally, switching from internal memory to SD memory means touching the camcorder's options menu - which can be a challenge at the far end of a camera crane.

And a couple of questions...

Which camera crane? All are weight rated and while I doubt we'll find a camera in your price range that will exceed the weight ratings of a decent crane, I'd just like to be sure. And the camera crane will be mounted to what? Are mics, lights, wireless receivers, shock mounts or other items expected to be on the crane, too?

Thinking through what is possible...

The "interchangeable lens" requirement is an odd one, but can be used to quickly filter.

There are two ways to do this. Since many camcorders are fixed-lens, one merely needs to add a DoF adapter to whichever camcorder you want to use (the camcorder needs filter-mounting threads). The DoF adapter provides the interchangeable lens capability. Since most of the camcorders in your price range don't have large 3CCD or 3CMOS imaging chip arrays when combined with their fixed lens, low light can be an issue - however, adding a DoF adapter can result in the lens pulling in more light compensating for the small imaging chip. Letus, EnCinema and a few others make these lens adapters. The lower end adapters turn the captured image upside down, so different workarounds to compensate are needed. Turn the camcorder upside down when capturing video or just rotate the image in post... or spend more for the lens adapter that does not flip the image.

If a lens adapter is not allowed, then the devices with an actual interchangeable lens system need to be identified and researched.

The Sony NEX-VG series is one of the "low end" camcorders with an interchangeable lens system - but no XLR audio inputs (unless an XLR adapter is used), no firewire, no LANC, no component out and some describe the NEX VG series as dSLRs designed to capture video. I believe the currently available units with a lens are well outside your budget.

The Canon EOS C100 Cinema Cam has XLR audio inputs, no firewire, no component video out, does not do 720p (but your video editor or other transcoder can easily take care of this externally), has a LANC but whether it can control the focus or zoom is unknown and likely depends on the lens. The body-only configuration is more than 2x your stated budget so adding lenses takes this well out of reach.

Blackmagic Design makes several "Cinema Cam" products. The Pocket Cinema Cam (is not yet available, but soon to be released and available for pre-order) is in your price range - without a lens - but no XLR audio inputs (unless an XLR adapter is used), no firewire, no component video out... and does have a LANC port assuming the lens used can be controlled through that LANC. It does not have a hot shoe. Lenses can easily take you beyond your stated budget.