Sounds like you got things figured out.
As far as that plug adapter goes, I wouldn't chance it. That third prong is an essential part of the circuit making it less hazardous. If a wire were to come loose inside your ballast and touch the case, it would shock the living shit out of you when you...
Man, I wasn't much of a grower when I started. Now, I'm in my own house trying to get my lawn looking good, get the flower bed looking good, got tomatoes growing in pots, gonna build a sectioned raised garden next year... it's endless now... but I like it. :)
And let me tell ya, smokin' your...
If you don't mind doing a little roof work, you could vent it through to a bathroom vent. Maybe through a soffit or directly out the roof if your soffit is vented.