Great options all! Thanks for the lively discussion and good ideas.
Am I right, though, that an IGP solution is going to use a lot less power than a dedicated solution? Lower power use = longer battery, after all!
No, you're not correct. It's more complicated than that.
Massive Oversimplification Follows:
Look up the specs of the machine and compare the combined TDPs of the CPU+GPU vs. the CPU/IGP. That's not 100% right, but it will give you an idea of the absolute skull-fucking maximum power draw. (In typical use, power draw will be much, much lower.)
Then you compare that to the watt-hours or milliamp-hours of the battery (battery capacity.)
Example 1: My laptop has an i7-4750HQ CPU/IGP, with a maximum TDP of 47w, and an 8700mAh 12v battery (about 100 watt hours). That will power the CPU at full load for 2 hours. (More like 90 minutes with the monitor and everything else, but we're going to ignore that going forward.)
Example 2: The Toshiba C55D-A5108 has an A6-5200 CPU/IGP. That will burn 25w maximum. However, the battery capacity is 48 watt-hours, so the battery life at 100%, full-on-worst-case-screw-you load is around the same.
Example 3: The Acer Aspire V3-572G-54S6 linked previously has an i5-4210U (15W TDP) and a GeForce 840m (33w) which, at 48w combined, is pretty close to Example 1. However, the battery is only 5000mAh, so the battery life would be <2/3rds as good. But it's because of the battery size, not because of the discrete GPU.