No problem with dive at all, balance is fine. I'm wondering why people say that about them.
When they first came out, depending on the body wood, they were reported to have balance issues. FWIW, the ASAT is essentially the same bass as the L-2000, with a different body and profile. I still remember when the semi-hollow body version came out. There were only about a dozen early on, and they were highly sought after. I remember trying the G&L line when they first came out, and wished I could have afforded one. Years later, it was on the vintageguitars site that discussion about how undervalued the G&L basses were got me thinking I should get one. My first encounter with The Dude was on an Ebay offering of an L-1000 that didn't meet reserve. I had emailed him, but he didn't get back to me. No harm, no foul. I finally got one, and I discovered the original Dudepit. The rest is history.