"Should I give the HDD it's own 5V line from the 1290 or just keep it on the PC"
Sorry if i misunderstood, but how is the laptop hd recieving its power now ? If there is other devices on the same power cable as it, that really shouldnt matter. but you could check for a voltage drop i suppose.
Also keep in mind that when you first turn on most devices they use more power.
and keep in mind the power calc is just a rough estimate.
If you have a regular high watt ac-dc psu, i'd try that and make sure everything runs fine for more than 15 minutes or so.
When you say the HDD reboots do you mean the whole pc?