Hi there, I have been doing wedding videography for few months now, and I think its time for me to pick up my 2nd camera. At the moment I am shooting with a HVR -V1U. Although I think its a fine camera, it isn't great under low light situations.
Therefore I am looking to see if I can pick up another Video Camera around the 4-5 thousand range that will give me great footage under low light conditions. Also I don't like the focus ring on the V1U so a better one an a different camera would be great.
The Sony EX1 is close to your budget (~$6000) and has 1/2" chips which should give better low light performance (I heard it may be discontinued, so there may be a new improved model soon or you may be able to get remaining stock at a bargain).
Also, you could consider a video DSLR like the Canon 5D mkII... I've been playing with some concert footage shot by a friend recently and low-light crowd shots were impressive to say the least. You can get very fast prime lenses for them which get you close to "see-in-the-dark" territory, and it would be way under your budget. The cameras do have a lot of other compromises though (awkward handling, very narrow focus if you're not used to it, useless onboard audio, etc). All that being said, it's certainly the wave of the future and takes killer stills too.
The Ex1 is a bit pricer than your specs. You also need to fact in cards to record to.
The Sony HVR Z5u would be a pretty good bet. Although not quite as good as the EX1 or 3 in low light, it is a very close second. And, the Z5u has much better ergonomics for hand-held work. Currently $4,250at B&H. (Get at least one extra battery.) I suspect that it will put your existing camera to some shame, though the V1u in bright light will hold up OK. If I were buying a doc camera, this would be my first choice. (Others will have other first choices...) (http://www.bhphotovideo.com/c/product/582905-REG/Sony_HVR_Z5U_HVR_Z5U_HDV_1080p_24p_CAMCORDER.html#reviews)
If you want to move over to tapeless, then a jump to the $5,200 Panasonic HPX170 might work for you. (http://www.bhphotovideo.com/c/product/559333-REG/Panasonic_AG_HPX170_AG_HPX170_P2HD_Solid_State_Camcorder.html#reviews)