How long can the FS700 shot continuously on a single stock battery? The 970?
Assuming you pressed the button and let it sit there.

I'm being asked to shoot about two hours of continuos footage and I haven't tested the camera that duration yet.

If it's a new genuine Sony NP-F970 or decent quality replacement battery of similar spec you will get more way more than two hours. Last couple of times I shot music shows without stopping the run times were about 150 minutes and the genuine batteries were indicating something like about 120 minutes to go. In fact the 700 is pretty frugal with batteries. Just one warning. After market batteries will indicate something insane like 700 minutes or something but when they go, well before that they go from 100% to “Hello I’m flat!” within a very short time. The Sony genuine batts will give you a more realistic accurate time scale to flat.
Chris Young
CYV Productions
Sydney

Shot 2 solid hours with NP-970 without issues, ended up around 40% (not even close to draining the battery).