On PIAA and HID bulbs...
This is purely my own personal bias and a subjective statement, but I think PIAA is highly over-rated. They've managed to develop a lot of brand recognition but most of their offerings, IMHO, are more sizzle than steak. They make lots of claims about how great the bulbs and lights are, that they have magic colors, and on and on. I've never seen a PIAA light installation that left me thinking it did something worth all the hoopla.
It's not hard to find bulbs being offered as "HID" or "xenon" lights when, in fact, they're simply not arc-lit HID systems. Maybe the PIAA HID bulbs mentioned above are spares for an HID-with-ballast system, but my inherent lack of faith in PIAA leaves me wondering if the claims are ...ah... a bit fanciful. Maybe not.
In any case, my criteria for "is it HID or not" comes down to "is there a high voltage power supply, and does the bulb produce illumination by striking an arc". When considering a replacement light source, if the answer to both questions isn't "yes", it ain't HID.
On wiring issues...
Agreed that the wiring harness, particularly the ground lead, for the headlights seems undersized for the job. The individual supply lines only supply about 3A when the lights are running, but the ground lead returns the full load, 6A. With HID's briefly drawing 6A each
as the arc is struck, the worst case current in the return becomes 12A+. There's something to be said for looking into beefing up the wire and using relays to control power supplied from the battery instead of the existing wiring harness.