How much video can be recorded on the new iPad?

A better question is to ask what the average data recording rate is. Based upon that you can calculate whatever limits you desire.

I've recorded a few short clips, in the neighborhood of 10-30 seconds, and from that and the resulting file size I calculate that 1080p recording requires roughly 2.8 MB/sec, or 168 MB/min, or 10 GB/hr.

You should be able to figure out whatever you need from that. Of course, these numbers are based upon the videos I've taken with my new iPad. YMMV.

This is dependent on what storage capacity you bought and what other content is stored on the device.

Esentially the amount of space that you see is available. You are only limited by the storage capacity of the iPad. I think the actual capacity comes around 14GB on that model.