What have you found so far?

Do the XLR connectors need to be built-in or can they be added?

Your requirements read low-end Pro. Prosumers don't normally use XLR connectors.

"Full 1920 x 1080p HD Resolution" and "High Definition Video Capture" are redundant.

My "normal" response" is that there is no pro-grade camcorder under $2,000. This assumes we agree to define "pro" as:
70mm lens or larger filter diameter;
1/3" or larger 3CCD or 3CMOS imaging chip;
XLR audio connectors;
Low compression video capture/storage.

Start at the Sony HVR-Z5. If the XLR connector requirement is relaxed, then the Sony HDR-FX1000. I understand the Canon XF100 or XF300 get in. But these, along with the Black Magic Cinema Cam (no XLR), and Canon Cinema EOS cams (add lenses) are well outside your budget. The Canon Cinema EOS cameras are not dSLRs and do not have the overheating issues dSLRs have.

If we are locked to your budget (and assume tripod and other steadying devices - including crane, lights, mics, cases, dolly, cables, LANC, and all the other stuff is covered under separate budgets), the closest I can get is the Sony HDR-FX7+XLR adapter as HDV/miniDV tape/1920x1080i. A Firestore or Sony external memory device can use the DV connection.

I don't understand what you mean by "SD recording over DV as it is more economically feasible". An 8-pack of Sony Premium miniDV tapes is $28 at Fry's. Please define your video archive plans.

As far as I know, all camcorders can connect to an external monitor via AV-out. At the higher end, RGB and HDMI monitoring is available.

There is no difference in video quality or resolution because of the storage media used. Assuming the video format is the same, the zeros and ones stored on the media are the same. If the video format is different (and different codes are used), then the potential exists for variation in video quality. A 25 mbps HDV file stored on miniDV tape and a 25 mbps HDV file store on flash memory (whether Firestore, Sony external video storage or SD card) is the same 25 mbps HDV file.

If you have the budget to buy a Firestore (actually, now "Vitec" Focus FS-H200 Pro), just add that $ to the camera budget. This might get you to the HDR-FX1000.